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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstraß \(\wp\)-function; Mordell's theorem; Hasse's theorem; \(L\)- function; Birch and Swinnerton-Dyer conjecture; \(j\)-invariant; rational points of elliptic curves; imaginary quadratic fields; Taniyama-Weil conjecture Henri Cohen, Elliptic curves, From number theory to physics (Les Houches, 1989) Springer, Berlin, 1992, pp. 212 -- 237. Elliptic curves, Rational points, Elliptic curves over local fields, Elliptic curves over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Elliptic curves | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic diophantine equations; equations over finite fields; arithmetic theory of algebraic curves; nonstandard arithmetic; zeta function; integral points on curves S. A. Stepanov, \textit{Arithmetic of Algebraic Curves} (Nauka, Moscow, 1991) [in Russian]. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Curves over finite and local fields, Arithmetic ground fields for curves, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Rational points Arithmetic of algebraic curves. | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic number theory; valuation theory; local class field theory; algebraic number fields; algebraic function fields of one variable; Riemann-Roch theorem E. Artin, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967. Research exposition (monographs, survey articles) pertaining to number theory, Class field theory, Class field theory; \(p\)-adic formal groups, Ramification and extension theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Collected or selected works; reprintings or translations of classics Algebraic numbers and algebraic functions | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic rank of elliptic curves; theorem of Lutz-Nagel; \(2\)-descent; families of elliptic curves; arithmetic function; quartic diophantine equation Elliptic curves over global fields, Other results on the distribution of values or the characterization of arithmetic functions, Elliptic curves Families of elliptic curves of rank \(\geq 1\) and remarks on an arithmetic function associated to an algorithm of 2-descent of Tate | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Fermat last theorem; survey; Fermat's equation; elliptic curve; conjecture of Szpiro; abc-conjecture; Serre's conjecture; existence of a cusp form of weight 2 for \(\Gamma _ 0(2)\); Taniyama-Weil conjecture; theorems of Mazur and Ribet; modular representation Oesterlé ( J. ) .- Nouvelles approches du ''théorème'' de Fermat , Séminaire Bourbaki n^\circ 694 (1987-88). Astérisque 161 -162, 165 - 186 ( 1988 ) Numdam | MR 992208 | Zbl 0668.10024 Higher degree equations; Fermat's equation, Elliptic curves over global fields, Galois representations, Special surfaces New approaches to Fermat's Last Theorem | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic valued function fields; good reduction; regular functions; reciprocity lemma; unit; local symbols; local-global principle; solvability of diophantine equations P. Roquette, \textsl Reciprocity in valued function fields, Journal für die reine und angewandte Mathematik 375/376 (1987), 238--258. Arithmetic theory of algebraic function fields, Valued fields, Algebraic functions and function fields in algebraic geometry, Diophantine equations Reciprocity in valued function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic functions in two variables; Riemann-Roch theorem; function fields Heinrich W. E. Jung, Einführung in die Theorie der algebraischen Funktionen zweier Veränderlicher, Akademie Verlag, Berlin, 1951 (German). Arithmetic theory of algebraic function fields, Research exposition (monographs, survey articles) pertaining to number theory, Algebraic functions and function fields in algebraic geometry Einführung in die Theorie der algebraischen Funktionen zweier Veränderlicher | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann surfaces; Abelian integrals; algebraic number theory; function fields; valuations; function fields of curves; Abel-Jacobi theorem Cohn, P. M.: Algebraic numbers and algebraic functions, Chapman \& Hall math. Ser. (1991) Algebraic number theory: global fields, Arithmetic theory of algebraic function fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Algebraic functions and function fields in algebraic geometry Algebraic numbers and algebraic functions | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic shrinking target problem; excursion rates of orbits; Jarník-Besicovitch theorem; Diophantine approximation; Heisenberg groups Homogeneous flows, Metric theory, Homogeneous approximation to one number, Harmonic analysis on homogeneous spaces, Homogeneous spaces and generalizations A shrinking target problem with target at infinity in rank one homogeneous spaces | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic first order theory of function fields in the language of fields; curves; undecidability Jean-Louis Duret, Sur la théorie élémentaire des corps de fonctions, J. Symbolic Logic 51 (1986), no. 4, 948 -- 956. Model-theoretic algebra, Model theory of fields, Decidability and field theory, Curves in algebraic geometry Sur la théorie élémentaire des corps de fonctions. (On the elementary theory of function fields) | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic diophantine geometry; height functions; rational points; abelian varieties; Mordell-Weil theorem; diophantine approximation; Roth's theorem; Siegel theorem; Bombieri's proof of Mordell's conjecture Hindry, Marc; Silverman, Joseph H., Diophantine geometry\upshape, An introduction, Graduate Texts in Mathematics 201, xiv+558 pp., (2000), Springer-Verlag, New York Arithmetic algebraic geometry (Diophantine geometry), Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Arithmetic problems in algebraic geometry; Diophantine geometry, Abelian varieties of dimension \(> 1\), Approximation to algebraic numbers, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Heights, Rational points, Global ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for abelian varieties Diophantine geometry. An introduction | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic recursively axiomatized class; pseudo real closed fields; strongly pseudo real closed; totally transcendental; totally real; Hilbertian fields; Hilbert's irreducibility theorem; model complete; model companionable; elimination of quantifiers; decidable; orderings; Nullstellensätze; function field; holomorphy ring; Prüfer ring; generalized Jacobson ring; p-adically closed fields DOI: 10.1007/BF03322485 Field extensions, Model theory of fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Relevant commutative algebra, Decidability of theories and sets of sentences, Model-theoretic algebra, Ordered fields, Quantifier elimination, model completeness, and related topics, Algebraic number theory: local fields, Dedekind, Prüfer, Krull and Mori rings and their generalizations On some classes of Hilbertian fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Witt rings of function fields; real analytic manifold; second residue class homomorphism; Artin-Lang property; Witt group of the ring of real analytic functions Algebraic theory of quadratic forms; Witt groups and rings, Real-analytic and semi-analytic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) On Witt rings of function fields of real analytic surfaces and curves | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Drinfeld modules; elliptic modules; cyclotomic function fields; congruence function fields; Carlitz modules; nonarchimedean analysis; explicit class field theory; Gauss sums; Gamma and Zeta functions and values; Jacobi sums; diophantine approximation; \(t\)-modules; \(t\)-motives; transcendence and irrationality; automata and algebraicity D.S. Thakur, \(Function Field Arithmetic\), World Scientfic, Singapore, 2004. Research exposition (monographs, survey articles) pertaining to number theory, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Curves over finite and local fields, Transcendence (general theory), Zeta and \(L\)-functions in characteristic \(p\), Class field theory, Other character sums and Gauss sums, Arithmetic theory of polynomial rings over finite fields, Arithmetic ground fields (finite, local, global) and families or fibrations, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic ground fields for curves Function field arithmetic | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Semi-stable and stable vector bundles on regular projective curves; moduli space of stable bundles; local non-abelian zeta functions for curves defined over finite fields (rationality and functional equations); global non-abelian zeta functions for curves defined over number fields; non-abelian L--functions for function fields (rationality and functional equations) Weng, L.: Non-abelian L function for number fields Zeta and \(L\)-functions in characteristic \(p\), Other Dirichlet series and zeta functions, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Vector bundles on curves and their moduli Non-abelian zeta functions for function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic points; Diophantine approximation; Schmidt's subspace theorem; Vojta's main conjecture Schmidt Subspace Theorem and applications, Global ground fields in algebraic geometry, Diophantine inequalities, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Heights On arithmetic inequalities for points of bounded degree | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic inter-universal Teichmüller theory; arithmetic deformation; key conjectures in Diophantine geometry; fundamental groups; mono-anabelian geometry; nonarchimedean theta function and its special values; deconstruction and reconstruction of ring structures; theta-links; log-theta-lattice Arithmetic algebraic geometry (Diophantine geometry), Rational points, Elliptic curves over global fields, Fine and coarse moduli spaces, Arithmetic varieties and schemes; Arakelov theory; heights Arithmetic deformation theory via arithmetic fundamental groups and non-Archimedean theta-functions, notes on the work of Shinichi Mochizuki | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic efficiency of function field sieve; discrete logarithms in finite fields; supersingular elliptic curves Granger, R., Holt, A., Page, D., Smart, N.P., Vercauteren, F.: Function field sieve in Characteristic three.In: Algorithmic Number Theory Symposium - ANTS VI, pp. 223--234. Springer LNCS 3076 (2004) Algebraic coding theory; cryptography (number-theoretic aspects), Number-theoretic algorithms; complexity, Applications to coding theory and cryptography of arithmetic geometry, Cryptography Function field sieve in characteristic three | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic central division algebras; anisotropic orthogonal involutions; Springer-Satz for orthogonal involutions; quadratic forms; motives of quadrics; function fields; Brauer-Severi varieties; Witt index; Chow motives А. С. Меркурьев, А. А. Суслин, \textit{K-когомологии многообpaзий Севери-Брауэра и гомоморфизм норменного вычета}, Изв. АН СССР, cep. мат \textbf{46} (1982), no. 5, 1011-1046. Engl. transl.: A. Merkurjev, A. Suslin, \textit{K-cohomology of Severi\(-\)Brauer varieties and the norm residue homomorphism}, Math. of the USSR-Izvestiya \textbf{21} (1983), 2, 307-340. Finite-dimensional division rings, Algebraic theory of quadratic forms; Witt groups and rings, Rings with involution; Lie, Jordan and other nonassociative structures, \(K\)-theory of quadratic and Hermitian forms, (Equivariant) Chow groups and rings; motives, Rational and birational maps On anisotropy of orthogonal involutions | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Drinfeld quasi-modular forms; Hankel determinants; function fields of positive characteristic Modular forms associated to Drinfel'd modules, Global ground fields in algebraic geometry, Formal groups, \(p\)-divisible groups Hankel-type determinants and Drinfeld quasi-modular forms | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Mickelsson-Faddeev cocycle; existence of string structures; bundle gerbe; quantum field theory; Atiyah-Patodi-Singer index theory; bundle of fermionic Fock spaces; gauge group action; Dixmier-Douady class; fermions in external fields; APS theorem; WZW model; Riemann surfaces; global Hamiltonian anomalies A. Alan Carey, A. Mickelsson, and M. Murray, ''Bundle gerbes applied to quantum field theory,'' hep-th/9711133. Quantum field theory; related classical field theories, Applications of global differential geometry to the sciences, Moduli problems for topological structures, Applications of PDEs on manifolds, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Generalizations of fiber spaces and bundles in algebraic topology Bundle gerbes applied to quantum field theory | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(\ell\)-adic cohomology; independence of \(\ell \); grothendieck's trace formula; Lefschetz trace formula; zeta functions over finite fields; Euler-poincaré characteristic; Betti number; bloch's conductor conjecture; intersection cohomology; grothendieck's six operations; intermediate extension; Weil conjectures; Hodge polygon; Newton polygon; crystalline cohomology; Hodge filtration; coniveau filtration; alteration; Fano variety; rationally connected; Weil group; swan conductor; wild ramification; Brauer trace; log scheme; logarithmic differential forms; Čebotarev's density theorem; semisimple group; fatou's Lemma Illusie, L.: Miscellany on traces in \(\mathcall \)-adic cohomology: a survey. Japan J. Math. \textbf{1}(1), 107-136 (2006). Erratum: Japan J. Math. \textbf{2}(2), 313-314 (2007) Étale and other Grothendieck topologies and (co)homologies, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Linear algebraic groups over arbitrary fields Miscellany on traces in \(\ell\)-adic cohomology: a survey | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic determinant method; arithmetic geometry Counting solutions of Diophantine equations, Varieties over global fields, Heights, Rational points Uniform bounds for the number of rational points on varieties over global fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic elliptic curves over function fields; explicit computation of \(L\)-functions; special values of \(L\)-functions and BSD conjecture; estimates of special values; analogue of the Brauer-Siegel theorem Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Zeta and \(L\)-functions in characteristic \(p\) Explicit \(L\)-functions and a Brauer-Siegel theorem for Hessian elliptic curves | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic function fields; finite field of constants; Severi's algebraic theory of correspondences; Hurwitz's transcendental theory; group of divisor classes; Riemann hypothesis for function fields; action of Galois group André Weil, Sur les fonctions algébriques à corps de constantes fini, C. R. Acad. Sci. Paris 210 (1940), 592 -- 594 (French). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves, Finite ground fields in algebraic geometry Sur les fonctions algébriques à corps de constantes fini | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic discriminant of splitting fields of principal homogeneous spaces; finiteness for the Tate-Shafarevich group of an elliptic curve; Arakelov intersection theory; effective divisor; Faltings Riemann-Roch theorem Paul Hriljac, Splitting fields of principal homogeneous spaces , Number theory (New York, 1984-1985), Lecture Notes in Math., vol. 1240, Springer, Berlin, 1987, pp. 214-229. Special algebraic curves and curves of low genus, Riemann-Roch theorems, Homogeneous spaces and generalizations, Elliptic curves, Divisors, linear systems, invertible sheaves Splitting fields of principal homogeneous spaces | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(p\)-extensions of algebraic function fields; Artin-Schreier theory; characteristic \(p\); genus; number of rational points; coding theory; gap number Arnaldo Garcia and Henning Stichtenoth, Elementary abelian \(p\)-extensions of algebraic function fields, Manuscr. Math. 72 (1991), 67--79. Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Geometric methods (including applications of algebraic geometry) applied to coding theory, Riemann surfaces; Weierstrass points; gap sequences, Computational aspects of algebraic curves Elementary abelian \(p\)-extensions of algebraic function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic fields of meromorphic function; Mittag-Leffler theorem; Weierstrass theorem P. Cutillas Ripoll,Construction of certain function fields associated with a compact Riemann surface, American Journal of Mathematics106 (1984), 1423--1450. Compact Riemann surfaces and uniformization, Algebraic functions and function fields in algebraic geometry Construction of certain function fields associated with a compact Riemann surface | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Artin approximation; Tougeron approximation; analytic/algebraic/power series equations; implicit function theorem; germs of differentiable functions Étale and flat extensions; Henselization; Artin approximation, Power series rings, Local deformation theory, Artin approximation, etc., \(C^\infty\)-functions, quasi-analytic functions Approximation results of Artin-Tougeron-type for general filtrations and for \(C^r\)-equations | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic anabelian geometry; pro-\(\ell \) groups; Galois theory; function fields; valuations theory; (Riemann) space of prime divisors; Hilbert decomposition theory; Parshin chains; decomposition graphs Pop, F., Recovering function fields from their decomposition graphs, 519-594, (2012), New York Field arithmetic, Separable extensions, Galois theory, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Algebraic functions and function fields in algebraic geometry Recovering function fields from their decomposition graphs | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(\lambda \)-structure of algebraic K-theory; vanishing theorem for intersection multiplicities; action of the Frobenius; Euler characteristic; Chow groups Gillet, H.; Soulé, C., Intersection theory using Adams operations, Invent. Math., 90, 243-277, (1987) Applications of methods of algebraic \(K\)-theory in algebraic geometry, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) Intersection theory using Adams operations | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann hypothesis; global function fields; zeta function in characteristic \(p\), Emil Artin; Helmut Hasse; André Weil; Friedrich Karl Schmidt; Max Deuring Research exposition (monographs, survey articles) pertaining to number theory, History of number theory, History of algebraic geometry, Arithmetic theory of algebraic function fields, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, History of mathematics in the 20th century, Sociology (and profession) of mathematics, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Algebraic functions and function fields in algebraic geometry The Riemann hypothesis in characteristic \(p\) in historical perspective | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Seshadri constants; Diophantine approximation; function fields; Schmidt Subspace Theoerm Rational points, Arithmetic varieties and schemes; Arakelov theory; heights Diophantine approximation constants for varieties over function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic geometric Langlands program; Langlands correspondence for function fields; moduli stack of \(G\)-bundles; Drinfeld-Lafforgue-Vinberg compactification; singularities of the degeneration; miraculous duality of Drinfeld and Gaitsgory; Drinfeld-Wang strange invariant bilinear form S. Schieder, Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg degeneration for \(\text{SL}_{2}\), Duke Math. J. 167 (2018), 835--921. Geometric Langlands program (algebro-geometric aspects) Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg degeneration for \(\mathrm{SL}_2\) | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic failure of Bertini's theorem; singular fibration in positive characteristic Stöhr, K. -O.: On Bertini's theorem in characteristic p for families of canonical curves in \(P(p - 3)/2\). Proc. lond. Math. soc. (3) 89, 291-316 (2004) Families, moduli of curves (algebraic), Singularities of curves, local rings, Arithmetic ground fields for curves, Projective techniques in algebraic geometry On Bertini's theorem in characteristic \(p\) for families of canonical curves in \(\mathbb{P}^{(p-3)/2}\) | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic integers; approximate equidistribution; Deligne's equidistribution theorem; Tate twist of Kloosterman sheaf; monodromy group; finite fields; number field; lattice; Minkowski embedding; Kloosterman sums; generalized Kloosterman sums in several variables Fisher, B., Kloosterman sums as algebraic integers, Math. Ann., 301, 1, 485-505, (1995) Other character sums and Gauss sums, Gauss and Kloosterman sums; generalizations, Finite ground fields in algebraic geometry, Varieties over finite and local fields, Étale and other Grothendieck topologies and (co)homologies, Algebraic numbers; rings of algebraic integers Kloosterman sums as algebraic integers | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Drinfeld modules; L-series; elliptic curve; q-expansion coefficients; Poisson kernel formula; space of cusp forms; non-archimedean measure; rigid analytic space; rigid analytic modular forms for function fields; Mellin transform J. T. Teitelbaum, The Poisson kernel for Drinfeld modular curves , J. Amer. Math. Soc. 4 (1991), no. 3, 491-511. JSTOR: Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, \(p\)-adic theory, local fields, Local ground fields in algebraic geometry, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Formal groups, \(p\)-divisible groups, Arithmetic theory of polynomial rings over finite fields The Poisson kernel for Drinfeld modular curves | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(L\)-series of number fields; infinite-dimensional analogue of one- parameter group; Artin formalism; self-adjoint operator; associated heat kernel; characteristic kernel; trace; asymptotic expansion; regularized determinant of the Laplacian; Selberg zeta function; theta functions J. Jorgenson, S. Lang, Artin formalism and heat kernels. Jour. Reine. Angew. Math. 447 (1994), 165-280. Zbl0789.11055 MR1263173 Other Dirichlet series and zeta functions, Spectral theory; trace formulas (e.g., that of Selberg), Heat and other parabolic equation methods for PDEs on manifolds, Theta functions and curves; Schottky problem, Langlands \(L\)-functions; one variable Dirichlet series and functional equations, Zeta functions and \(L\)-functions of number fields, Theta functions and abelian varieties Artin formalism and heat kernels | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic translations of classics (algebraic geometry); history of algebraic geometry; mathematics of the 19th century; algebraic functions; function fields; algebraic curves; Riemann-Roch theorem; algebraic differential 2.R. Dedekind, H. Weber, \(Theory of algebraic functions of one variable.\) Translated from the 1882 German original and with an introduction, bibliography and index by John Stillwell. History of Mathematics, 39. American Mathematical Society (Providence, RI; London Mathematical Society, London, 2012), pp. viii+152 History of algebraic geometry, Biographies, obituaries, personalia, bibliographies, Algebraic functions and function fields in algebraic geometry, History of mathematics in the 19th century, Arithmetic theory of algebraic function fields, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials Theory of algebraic functions of one variable. Transl. from the German and introduced by John Stillwell | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann hypothesis for curves; Weil explicit formulas; zeros of Riemann zeta-function; Riemann-Roch theorem; supersymmetry; Riesz potentials; compact Riemannian manifold; Atiyah-Singer index theorem Haran, Shai, Index theory, potential theory, and the Riemann hypothesis.\(L\)-functions and arithmetic, Durham, 1989, London Math. Soc. Lecture Note Ser. 153, 257-270, (1991), Cambridge Univ. Press, Cambridge Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), \(\zeta (s)\) and \(L(s, \chi)\) Index theory, potential theory, and the Riemann hypothesis | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic self-dual codes; algebraic geometry codes; Gilbert-Varshamov bound; Tsfasman-Vladut-Zink bound; towers of function fields; asymptotically good codes; quadratic forms; Witt's theorem Applications to coding theory and cryptography of arithmetic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory Self-dual codes better than the Gilbert-Varshamov bound | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic finite fields; function field; hyperelliptic curve; moments of quadratic Dirichlet L-function; prime polynomial Andrade, J. C.; Keating, J. P., Mean value theorems for \textit{L}-functions over prime polynomials for the rational function field, Acta Arith., 161, 4, 371-385, (2013) Curves over finite and local fields, Zeta and \(L\)-functions in characteristic \(p\), Relations with random matrices, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Mean value theorems for \(L\)-functions over prime polynomials for the rational function field | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann-Roch formula for \(\ell\)-adic sheaves of rank one; \({\mathcal D}\)-module; invariants of wild ramification; ramification in finite coverings of higher dimensional schemes; Artin characters for higher dimensional regular local rings; class field theory; Serre's conjecture; ramification of Galois representations; Swan conductor; characteristic cycle K. Kato, Class field theory, \(D\)-modules, and ramification on higher-dimensional schemes, Part I, Amer. J. Math., 116, 757-784, (1994) Class field theory, Geometric class field theory, Generalized class field theory (\(K\)-theoretic aspects), Riemann-Roch theorems, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials Class field theory, \({\mathcal D}\)-modules, and ramification on higher dimensional schemes. I | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic transcendence of elliptic modular functions in characteristic \(p\); Tate elliptic curve; theorem of Siegel and Schneider; transcendence of periods of elliptic curves; Mahler-Manin conjecture; elliptic logarithm [V1] J. F. Voloch:Transcendence of elliptic modular functions in characteristic p, J. Number Theory58 (1996) 55-59. Transcendence theory of elliptic and abelian functions, Elliptic curves Transcendence of elliptic modular functions in characteristic \(p\) | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic resolution of singularities in positive characteristic; residual order; examples for infinite increase of residual order Global theory and resolution of singularities (algebro-geometric aspects), Singularities in algebraic geometry, Positive characteristic ground fields in algebraic geometry, Formal power series rings Cycles of singularities appearing in the resolution problem in positive characteristic | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic automorphism groups; cancellation problem for function fields; function fields of general type; Zariski problem Relevant commutative algebra, Surfaces and higher-dimensional varieties, Transcendental field extensions, Algebraic functions and function fields in algebraic geometry, Group actions on varieties or schemes (quotients), Arithmetic theory of algebraic function fields Automorphism groups of ruled functions fields and a problem of Zariski | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Conference; Diophantine approximation; Abelian varieties; Soesterberg (Netherlands); Faltings' theorem; Mordell's conjecture; abelian variety; set of rational points; diophantine approximation; diophantine algebraic geometry Edited by B. Edixhoven - J.-H. Evertse, Diophantine approximation and abelian varieties, Lecture Notes in Mathematics, vol. 1566, Springer-Verlag, Berlin (1993), Introductory lectures, Papers from the conference held in Soesterberg, April 12-16, 1992. Zbl0811.14019 MR1288998 Rational points, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Algebraic theory of abelian varieties, Varieties over global fields, Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to number theory, Proceedings, conferences, collections, etc. pertaining to algebraic geometry Diophantine approximation and abelian varieties. Introductory lectures. Papers of the conference, held in Soesterberg, Netherlands, April 12-16, 1992 | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic twin irreducible polynomials; parity barrier over function fields; short character sums; level of distribution for irreducible polynomials Étale and other Grothendieck topologies and (co)homologies, Arithmetic theory of algebraic function fields, Polynomials over finite fields, Goldbach-type theorems; other additive questions involving primes, Primes in congruence classes On the Chowla and twin primes conjectures over \(\mathbb{F}_q[T]\) | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic function fields; algebraic curves; Riemann-Roch theorem; coding theory; algebraic-geometry codes; differentials; towers of functions fields; Tsfasman-Vladut-Zink theorem; trace codes Stichtenoth, H., \textit{Algebraic Function Fields and Codes}, 254, (2009), Springer, Berlin Algebraic functions and function fields in algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects) Algebraic function fields and codes | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic curves over number fields; diophantine equations; symmetric power of algebraic curves; Mordell conjecture; Jacobian variety; geometric gap principle; arithmetic gap priciple; gap principle for abelian varieties; quadratic point Joseph H. Silverman, Rational points on symmetric products of a curve, Amer. J. Math. 113 (1991), no. 3, 471 -- 508. Rational points, Arithmetic ground fields for abelian varieties, Arithmetic ground fields for curves, Higher degree equations; Fermat's equation Rational points on symmetric products of a curve | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic curves defined over a valuation ring; function field; first order language of valued fields; stable reduction theorem [GMP] B. W. Green, M. Matignon and F. Pop,On valued function fields III, Reductions of algebraic curves, Journal für die Reine und Angewandte Mathematik432 (1992), 117--133. Arithmetic ground fields for curves, Valued fields, First-order arithmetic and fragments On valued function fields. III: Reductions of algebraic curves. Appendix (by Ernst Kani): The stable reduction theorem via moduli theory | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic group of automorphisms; birational splitting theorem for the Albanese map; Albanese variety; meromorphic function field Rational and birational maps, Automorphisms of curves, Birational automorphisms, Cremona group and generalizations, Automorphisms of surfaces and higher-dimensional varieties Meromorphic function fields of Albanese bundles | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic linear algebraic group; R-equivalence; function fields of surfaces; weak approximation; Hasse principle Colliot-Thélène, J.-L.; Gille, P.; Parimala, R., Arithmetic of linear algebraic groups over two-dimensional geometric fields, Duke Math. J., 121, 285-341, (2004) Forms of degree higher than two, Modular and Shimura varieties, Linear algebraic groups over adèles and other rings and schemes, Linear algebraic groups over arbitrary fields, Global ground fields in algebraic geometry Arithmetic of linear algebraic groups over 2-dimensional geometric fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic curves in characteristic p; set of points in uniform position; bounds for the genus of curves Jürgen Rathmann, The uniform position principle for curves in characteristic \?, Math. Ann. 276 (1987), no. 4, 565 -- 579. Enumerative problems (combinatorial problems) in algebraic geometry, Curves in algebraic geometry, Finite ground fields in algebraic geometry The uniform position principle for curves in characteristic p | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic affine variety minus bound on the height of integral points; hyperplanes in general position; number of integral points; function fields Wang, J.T.-Y., \textit{S}-integral points of \(\mathbb{P}^n - \{2 n + 1 \text{ hyperplanes in general position} \}\) over number fields and function fields, Trans. amer. math. soc., 348, 3379-3389, (1996) Arithmetic theory of algebraic function fields, Rational points, Varieties over global fields \(S\)-integral points of \(\mathbb{P}^ n- \{2n+1\) hyperplanes in general position\(\}\) over number fields and function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic real function fields; real holomorphy ring; valuation rings; formally real residue field; regular projective model; rational point; real prime divisors; signatures of higher level; sums of n-th powers; local-global principle; weak isotropy; quadratic forms; Henselizations Schülting, H. W.: The binary class group of the real holomorphy ring. (1986) Valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Forms over real fields, Real algebraic and real-analytic geometry, Valuations and their generalizations for commutative rings Sums of 2n-th powers in real function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic function fields of conics; Zariski problem; transcendental extension; rationality; regular function field; Amitsur-MacRae theorem Jack Ohm, Function fields of conics, a theorem of Amitsur-MacRae, and a problem of Zariski, Algebraic geometry and its applications (West Lafayette, IN, 1990) Springer, New York, 1994, pp. 333 -- 363. Transcendental field extensions, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Function fields of conics, a theorem of Amitsur-MacRae, and a problem of Zariski | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic computer algebra system SINGULAR; tangent cone algorithm; Gröbner basis; ideal in a polynomial ring; standard basis; invariants of the local ring of an algebraic variety; Hilbert's syzygy theorem; deformation; dimension; multiplicity; Hilbert function G. Greuel and G. Pfister, Advances and improvements in the theory of standars bases and syzygies, Arch. Math., 1906, 66: 163--176. Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Singularities in algebraic geometry, Computational aspects in algebraic geometry Advances and improvements in the theory of standard bases and syzygies | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic conjecture of Colliot-Thélène; Ax-Kochen theorem; Diophantine equations; \(p\)-adic numbers; forms in many variables; Diophantine geometry; monomialization; toroidalization of morphisms Local ground fields in algebraic geometry, Polynomials Proof of a conjecture of Colliot-Thélène and a Diophantine excision theorem | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic finite fields; number theory; algebraic geometry; permutation polynomials; multilinear equations; quadratic forms; characters; Gauss sums; Jacobi sums; diagonal equations; zeta function; Chevalley's theorem; law of quadratic reciprocity; Davenport-Hasse theorem; Fermat curve; elliptic curve Small, C.: Arithmetic of finite fields. Monogr. textbooks pure appl. Math. 148 (1991) Finite fields and commutative rings (number-theoretic aspects), Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Polynomials over finite fields, Quadratic forms over general fields, Other character sums and Gauss sums, Structure theory for finite fields and commutative rings (number-theoretic aspects), Finite ground fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Arithmetic of finite fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(S\)-units in function fields; complement of a conic and two lines; log Kodaira dimension Corvaja, Pietro; Zannier, Umberto, Some cases of Vojta's conjecture on integral points over function fields, J. Algebraic Geom., 1056-3911, 17, 2, 295\textendash 333 pp., (2008) Varieties over global fields, Elliptic curves over global fields, Global ground fields in algebraic geometry Some cases of Vojta's conjecture on integral points over function fields. | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic isogeny theorem for elliptic curves; translation formulas; positive upper bound for linear forms; heights; explicit lower bounds for linear forms in elliptic logarithms; elliptic curves; explicit bounds for the growth of the Weierstrass functions; derivation formulas David, S., Minorations de formes linéaires de logarithmes elliptiques, Mém. Soc. Math. France, 62, 1-143, (1995) Transcendence theory of elliptic and abelian functions, Linear forms in logarithms; Baker's method, Elliptic curves over global fields, Isogeny Lower bounds for linear forms in elliptic logarithms | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic function fields; class group; continued fractions; generalization of Hirzebruch's theorem; class number González, CD, Class numbers of quadratic function fields and continued fractions, J. Number Theory, 40, 38-59, (1992) Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Continued fractions, Jacobians, Prym varieties, Finite ground fields in algebraic geometry Class numbers of quadratic function fields and continued fractions | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Poincaré series for p-adic points on a variety; arithmetic theory of polynomials; Siegel-Weil formula; forms of higher degree; generalized Poisson formula; local zeta function; Bernshtein's theorem; Denef's theorem; rationality; zeta distributions; invariants for prehomogeneous vector spaces; poles Analytic theory (Epstein zeta functions; relations with automorphic forms and functions), Research exposition (monographs, survey articles) pertaining to number theory, Zeta functions and \(L\)-functions of number fields, Research exposition (monographs, survey articles) pertaining to field theory, Forms of degree higher than two, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Some aspects of the arithmetic theory of polynomials | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic natural Lagrangian system; monoidal transformation of real analytic manifold; normal crossing; logarithmic fields; inversion of Lagrange-Dirichlet theorem; critical point; analytic potential function; Lyapunov's problem; supercritical motions; Lagrangian system with gyroscopic forces Palamodov, V.P.: Stability of motion and algebraic geometry. In: Dynamical Systems in Classical Mechanics (Amer. Math. Soc. Transl. Ser. 2), vol. 168, 5--20 (1995) Stability for nonlinear problems in mechanics, Global theory and resolution of singularities (algebro-geometric aspects) Stability of motion and algebraic geometry | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic real function fields; real holomorphy ring; valuation rings; formally real residue field; regular projective model; rational point; real prime divisors; signatures of higher level; sums of n-th powers; Local-Global- Principle; weak isotropy; quadratic forms; Henselizations SCHÜLTING, H.W.: Prime divisors on real varieties and valuation theory. J. Alg.98, 499-514 (1986) Valued fields, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Forms over real fields, Real algebraic and real-analytic geometry, Valuations and their generalizations for commutative rings Prime divisors on real varieties and valuation theory | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic rational points; homogeneous polynomial; quasi-projective variety; Hilbert subset; algebraic cycle with rational coefficients; finite fields; rationality of the zeta function of Hilbert sets; Dwork's rationality theorem; decomposition theorem Wan, Daqing: Hilbert sets and zeta functions over finite fields, J. reine angew. Math. 427, 193-207 (1992) Varieties over finite and local fields, Finite ground fields in algebraic geometry, Hilbertian fields; Hilbert's irreducibility theorem, Algebraic cycles Hilbert sets and zeta functions over finite fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass statement; algebraic addition theorem; meromorphic functions; Picard varieties; continuation of closed subgroup; separately extendable meromorphic functions; algebraic function fields; quasi-abelian functions; extendable line bundles on toroidal groups Abe, Y., A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem, J. Math. Soc. Jpn., 57, 709-723, 07, (2005) Meromorphic functions of several complex variables, Abelian varieties and schemes A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Radon transform; second main theorem for holomorphic curves; Abelian varieties --, Holomorphic curves in abelian varieties: the second main theorem and applications.Japan. J. Math. (N.S.), 26 (2000), 129--152. Value distribution theory in higher dimensions, Analytic theory of abelian varieties; abelian integrals and differentials Holomorphic curves in abelian varieties: the second main theorem and applications | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic finiteness theorem; function field of characteristic \(p\); Mordell's conjecture; Manin-Mumford conjecture; Lang's conjecture Alexandru Buium and José Felipe Voloch, Lang's conjecture in characteristic \?: an explicit bound, Compositio Math. 103 (1996), no. 1, 1 -- 6. Rational points, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry, Global ground fields in algebraic geometry, Varieties over global fields Lang's conjecture in characteristic \(p\): An explicit bound | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic singular curves over finite fields; rationality of the zeta function; functional equation of the zeta function; singular Riemann-Roch theorem Galindo, W. Zúñiga: Zeta functions of singular algebraic curves over finite fields. (1996) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic ground fields for curves, Curves over finite and local fields, Jacobians, Prym varieties, \(\zeta (s)\) and \(L(s, \chi)\), Riemann-Roch theorems Zeta functions of singular curves over finite fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic effective algorithm for cuspidal modular function; Mazur-Tate conjecture; global field of characteristic \(p\); numerical calculation of \(L\); modular element Tan K.-S. and Rockmore D., Computation of L-series for elliptic curves over function fields, J. reine angew. Math. 424 (1992), 107-135. Computational aspects of algebraic curves, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry, Adèle rings and groups Computation of \(L\)-series for elliptic curves over function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic quadratic forms; numerical invariants of fields; level of a field; non-formally real fields; anisotropic quadratic form; formally real fields; \(u\)-invariants; Pythagoras number; existence of \(K\)-rational points for systems of forms; homogeneous Nullstellensatz for \(p\)-fields; Borsuk-Ulam Theorem; spheres; Tsen-Lang theory of \(C_ i\)-fields; computation of the levels of projective spaces; Witt rings A. Pfister, \textit{Quadratic forms with applications to algebraic geometry and topology}. London Mathematical Society Lecture Note Series, \textbf{217}. Cambridge University Press, Cambridge, 1995. zbl 0847.11014; MR1366652 Quadratic forms over general fields, Research exposition (monographs, survey articles) pertaining to number theory, Algebraic theory of quadratic forms; Witt groups and rings, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Skew fields, division rings, Classical topics in algebraic topology Quadratic forms with applications to algebraic geometry and topology | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic modular function fields; principal congruence subgroups of prime level; algorithm; Newton polygon N. Ishida, N. Ishii, The equations for modular function fields of principal congruence subgroups of prime level. Manuscripta Math. 90 (1996), no. 3, 271-285. Zbl0871.11031 MR1397657 Modular and automorphic functions, Algebraic functions and function fields in algebraic geometry The equations for modular function fields of principal congruence subgroups of prime level | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic second generalized Giulietti-Korchmáros function fields; maximal function fields; genus spectrum of maximal curves Curves over finite and local fields, Arithmetic ground fields for curves, Automorphisms of curves On subfields of the second generalization of the GK maximal function field | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic linear groups; real curves; projective curves; function fields; strong Hasse principle; homogeneous spaces; existence of \(K\)-rational points; weak approximation; density of local points; diagonal image; central isogeny; principal homogeneous spaces; projective algebraic varieties; reciprocity law; obstruction to the Hasse principle; obstruction to weak approximation; Galois cohomology Jean-Louis Colliot-Thélène, Groupes linéaires sur les corps de fonctions de courbes réelles, J. Reine Angew. Math. 474 (1996), 139 -- 167 (French). Galois cohomology of linear algebraic groups, Algebraic functions and function fields in algebraic geometry, Real algebraic and real-analytic geometry, Linear algebraic groups over adèles and other rings and schemes, Homogeneous spaces and generalizations Linear groups on the function fields of real curves | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic elliptic curves; cryptosystems; finite fields of odd characteristic; prime fields N. Smart, Elliptic curve cryptosystems over small fields of odd characteristic. \textit{J. Crypt.}~\textbf{12}, 141-151 (1999) Cryptography, Applications to coding theory and cryptography of arithmetic geometry, Elliptic curves over global fields Elliptic curve cryptosystems over small fields of odd characteristic | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic problems on singularities; Minkowski problem for nonconvex surfaces; mappings with mild singularities; vanishing inflections; multiplicities of fixed points of iterations; higher Painlevé equations; sphere neighborhoods; cycles of correspondences; zeroes of Abelian integrals; topology of trains in flag spaces; converse of a theorem of Archimedes; nonintegrable dynamical systems Arnol'd, V. I.: Ten problems. Adv. sov. Math. 1, 1-8 (1990) Research exposition (monographs, survey articles) pertaining to global analysis, Differentiable maps on manifolds, Theory of singularities and catastrophe theory, Global theory and resolution of singularities (algebro-geometric aspects), Global surface theory (convex surfaces à la A. D. Aleksandrov), Homotopy groups of special types, Critical points and critical submanifolds in differential topology, Fixed points and coincidences in algebraic topology, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Topological dynamics, Differential topological aspects of diffeomorphisms, Surfaces in Euclidean and related spaces, Rational and birational maps, Elliptic functions and integrals, Vector spaces, linear dependence, rank, lineability Ten problems | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic determinant of cohomology; theta function; embeddings for the moduli-spaces of abelian varieties; vector bundles on curves; étale cohomology; \(p\)-adic \(L\)-functions; vanishing Euler characteristic Étale and other Grothendieck topologies and (co)homologies, Theta functions and abelian varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) The determinant of cohomology in étale topology | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic equidistribution for pure sheaves; exponential sums; L-functions of varieties over finite fields; Kloosterman sums; Fourier transforms of monomials in Gauss sums; Kloosterman sheaves; local monodromy; convolution of sheaves; Swan conductor N.\ M. Katz, Gauss sums, Kloosterman sums, and monodromy groups, Ann. of Math. Stud. 116, Princeton University Press, Princeton 1988. Sheaves in algebraic geometry, Global ground fields in algebraic geometry, Exponential sums, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry Gauss sums, Kloosterman sums, and monodromy groups | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Monge-Ampère operator; local algebra; monomial ideal; Hilbert-Samuel multiplicity; log-canonical threshold; plurisubharmonic function; Ohsawa-Takegoshi \(L^2\) extension theorem; approximation of singularities; birational rigidity Demailly, J.-P., Estimates on Monge-Ampère operators derived from a local algebra inequality, (Passare, M., Complex Analysis and Digital Geometry, Proceedings from the Kiselmanfest, 2006, (2009), Uppsala University Uppsala, Sweden), 131-143 Complex Monge-Ampère operators, Plurisubharmonic exhaustion functions, Local complex singularities, Singularities in algebraic geometry, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry Estimates on Monge-Ampère operators derived from a local algebra inequality | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic arithmetic over function fields; arithmetic of algebraic curves; Mordell Weil theorem; Mordell conjecture Rational points, Global ground fields in algebraic geometry, Arithmetic ground fields for curves, Heights, Elliptic curves over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic theory of algebraic function fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry Diophantine geometry on curves over function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic forms over number fields; Hasse principle; affine variety; Hardy-Littlewood circle method; asymptotic formula; number of solutions; weak approximation C.\ M. Skinner, Forms over number fields and weak approximation, Compos. Math. 106 (1997), 11-29. Forms of degree higher than two, Applications of the Hardy-Littlewood method, Diophantine equations in many variables, Global ground fields in algebraic geometry, Varieties over global fields Forms over number fields and weak approximation | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic linear systems of curves; generality on pointsets in projective 2-space; very ample divisor; blowing-up a finite set of points; Cayley-Bacharach theorem Divisors, linear systems, invertible sheaves, Projective techniques in algebraic geometry, Families, moduli of curves (algebraic) Bese's very ampleness theorem and punctured complete intersections | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic analytic functions; analytic manifold of dimension one; real spectrum; Weierstrass theorem; approximation [An-Be] Andradas, C., Becker, E.: A note on the Real Spectrum of Analytic functions on an Analytic manifold of dimension one. Proceedings of the Conference on Real Analytic and Algebraic Geometry, Trento, 1988. (Lect. Notes Math. vol. 1420, pp. 1--21) Berlin Heidelberg New York: Springer 1990 Semi-analytic sets, subanalytic sets, and generalizations, Real-analytic and semi-analytic sets A note on the real spectrum of analytic functions on an analytic manifold of dimension one | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic groups; adjoint groups; R-equivalence; nondyadic local fields; function fields of curves; algebras with involution; Hermitian forms; Rost invariant R. Preeti and A. Soman, Adjoint groups over \Bbb Q_{\?}(\?) and R-equivalence, J. Pure Appl. Algebra 219 (2015), no. 9, 4254 -- 4264. Linear algebraic groups over local fields and their integers, Quadratic forms over general fields, Bilinear and Hermitian forms, Classical groups, Galois cohomology of linear algebraic groups, Rational points, Other nonalgebraically closed ground fields in algebraic geometry, Finite-dimensional division rings, Rings with involution; Lie, Jordan and other nonassociative structures Adjoint groups over \(\mathbb Q_p(X)\) and R-equivalence. | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic function field of positive characteristic; arithmetic fundamental group; Galois representation; automorphic representation G. Böckle and C. Khare, Finiteness results for mod \(l\) Galois representations over function fields, Galois representations, Representation-theoretic methods; automorphic representations over local and global fields, Coverings of curves, fundamental group, Galois cohomology Mod \(\ell\) representations of arithmetic fundamental groups. I: An analog of Serre's conjecture for function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic addition theorem for theta functions of Jacobian varieties; trilinear functional equations Бухштабер, В. М.; Кричевер, И. М., Интегрируемые уравнения, теоремы сложения и проблема римана--шоттки, УМН, 61, 1-367, 25-84, (2006) Theta functions and curves; Schottky problem, Relationships between algebraic curves and integrable systems, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions Integrable equations, addition theorems, and the Riemann-Schottky problem | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Hasse-Weil-Serre bound; zeta function of curves over finite fields; rational points K. Lauter, Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields, Institut de Mathématiques de Luminy, preprint, 1999, pp. 99--29. Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic ground fields for curves Improved upper bounds for the number of rational points on algebraic curves over finite fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Diophantine approximation; curves over finite fields; Vojta's conjecture Corvaja, P.; Zannier, U., Greatest common divisors of \(u - 1\), \(v - 1\) in positive characteristic and rational points on curves over finite fields, J. Eur. Math. Soc., 15, 1927-1942, (2013) Varieties over finite and local fields, Elliptic curves over global fields, Finite ground fields in algebraic geometry, Local ground fields in algebraic geometry Greatest common divisors of \(u-1, v-1\) in positive characteristic and rational points on curves over finite fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic abstract elliptic function fields; automorphisms; meromorphisms; addition theorem Hasse, H.: Zur theorie der abstrakte elliptischen funktionenkörper. II. automorphismen und meromorphismen. Das additionstheorem. J. reine angrew. Math. 175, 69-88 (1936) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Zur Theorie der abstrakten elliptischen Funktionenkörper. II: Automorphismen und Meromorphismen. Das Additionstheorem | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic finite groups; finite simple groups; applications of simple groups; Brauer groups; Riemann surfaces; polynomials; function fields Guralnick, Robert, Applications of the classification of finite simple groups.Proceedings of the International Congress of Mathematicians---Seoul 2014. Vol. II, 163-177, (2014), Kyung Moon Sa, Seoul Finite simple groups and their classification, Primitive groups, Coverings of curves, fundamental group, Algebraic field extensions Applications of the classification of finite simple groups | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic real algebraic geometry; real algebraic varieties; complexification; Smith's theory; Galois-Maximal varieties; algebraic cycles; real algebraic models; algebraic curves; algebraic surfaces; topology of algebraic varieties; regular maps; rational maps; singularities; algebraic approximation; Comessatti theorem; Rokhlin theorem; Nash conjecture; Hilbert's XVI problem; Cremona group; real fake planes Topology of real algebraic varieties, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Real algebraic and real-analytic geometry, Surfaces and higher-dimensional varieties, Curves in algebraic geometry, Varieties and morphisms, Special varieties Real algebraic varieties | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic difference field; abelian variety; theory ACFA; group definable in a model; model theoretic stability; 1-basedness; Manin-Mumford conjecture; model companion of the theory of fields with an automorphism Z. Chatzidakis, ''Groups definable in ACFA,'' in Algebraic Model Theory, Dordrecht: Kluwer Acad. Publ., 1997, vol. 496, pp. 25-52. Model-theoretic algebra, Applications of logic to group theory, Model theory of fields, Difference algebra, Classification theory, stability, and related concepts in model theory, Abelian varieties of dimension \(> 1\), Rational points Groups definable in ACFA | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic number of non-rational subfields; number of separable subfields; number of morphisms of algebraic curves; Chow coordinates; theorem of the base; Jacobian; genus; function field; Angle theorem; de Franchis' theorem E. Kani, Bounds on the number of non-rational subfields of a function field, Invent. Math. 85 (1986), 185-198. Zbl0615.12017 MR842053 Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Birational geometry, Jacobians, Prym varieties, Divisors, linear systems, invertible sheaves, Special surfaces Bounds on the number of non-rational subfields of a function field | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Hasse-Weil bound; trace code; Hamming weight; algebraic curves over finite fields of characteristic 2; number of points van der Geer, Gerard; van der Vlugt, Marcel, Curves over finite fields of characteristic 2 with many rational points, C. R. acad. sci. Paris Sér. I math., 317, 6, 593-597, (1993), MR 1240806 Finite ground fields in algebraic geometry, Curves over finite and local fields, Algebraic coding theory; cryptography (number-theoretic aspects), Rational points, Linear codes (general theory) Curves over finite fields of characteristic 2 with many rational points | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Tate module; Galois representation; analogue of Falting's semi-simplicity theorem; Shafarevich-type finiteness result; isogenies of Drinfel'd modules; heights \textsc{R.~Dedekind}\textsc{and}\textsc{H.~Weber}, Theorie der algebraischen Functionen einer Veränderlichen, J. Reine Angew. Math. \textbf{92} (1882), 181-290. Drinfel'd modules; higher-dimensional motives, etc., Isogeny, Abelian varieties of dimension \(> 1\), Curves over finite and local fields Semi-simplicity of the Galois representations attached to Drinfeld modules over fields of ``infinite characteristics'' | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic classification of Brauer groups; rational function fields over global fields; Ulm invariants B. Fein, M.M. Schacher and J. Sonn, Brauer groups of rational function fields, Bull. Amer. Math. Soc. 1, 766-768. Arithmetic theory of algebraic function fields, Galois cohomology, Transcendental field extensions, Brauer groups of schemes Brauer groups of rational function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic function fields; valuation; value group; rank; direct sum of n infinite cyclic groups MacLane, S. - Schilling, O.F.G.\(\,\): Zero-dimensional branches of rank 1 on algebraic varieties, Annals of Math. 40 (1939), 507-520 Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Valued fields Zero-dimensional branches of rank one on algebraic varieties | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic integral points; entire curves; hyperbolicity; Weil functions; Schmidt subspace theorem; second main theorem Heier, G; Ru, M, Essentially large divisors and their arithmetic and function-theoretic inequalities, Asian J. Math., 16, 387-407, (2012) Varieties over global fields, Heights, Divisors, linear systems, invertible sheaves, Arithmetic varieties and schemes; Arakelov theory; heights, Schmidt Subspace Theorem and applications, Value distribution theory in higher dimensions Essentially large divisors and their arithmetic and function-theoretic inequalities | 0 |
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