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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 towers of algebraic function fields; genus; number of places Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Quadratic recursive towers of function fields over \(\mathbb{F}_2\) | 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 moving cuspidal singularities; positive characteristic; fibration by p- closed rational vector fields; singularities of fibres; generalized Raynaud surface Takeda, Y.: Fibrations with moving cuspidal singularities. Nagoya Math. J.122, 161-179 (1991) Global theory and resolution of singularities (algebro-geometric aspects), Singularities of surfaces or higher-dimensional varieties, Families, fibrations in algebraic geometry, Singularities in algebraic geometry, Singularities of curves, local rings Fibrations with moving cuspidal singularities | 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 theory of genus 1 curves; local-global principle; rational points; heights; finite basis theorem; Tate-Shafarevich group; arithmetic of elliptic curves J.W.S. Cassels, \textit{Lectures on elliptic curves}, \textit{Lond. Math. Soc. Stud. Texts}\textbf{24}, Cambridge University Press, Cambridge, U.K., (1991). Elliptic curves, Rational points, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Special algebraic curves and curves of low genus Lectures on 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 Henselian rings; Weierstrass Preparation Theorem; Artin Approximation Theorem; elimination of quantifiers; deformation of isolated singularities; Weierstrass-Grauert Preparation Theorem H. Kurke, G. Pfister, D. Popescu, M. Roczen and T. Mostowski, Die Approximationseigenschaft lokaler Ringe, Lecture Notes in Math. 634, Springer, Berlin 1978. Local rings and semilocal rings, Research exposition (monographs, survey articles) pertaining to commutative algebra, Metamathematics of constructive systems, Henselian rings, Complete rings, completion, Formal methods and deformations in algebraic geometry, Deformations and infinitesimal methods in commutative ring theory Die Approximationseigenschaft lokaler Ringe | 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 degree of Igusa's local zeta function; resolution for a polynomial J. Denef, On the degree of Igusa's local zeta function , Amer. J. Math. 109 (1987), no. 6, 991-1008. JSTOR: Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Local ground fields in algebraic geometry, Zeta functions and \(L\)-functions On the degree of Igusa's local zeta function | 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 geometric codes; towers of function fields Geometric methods (including applications of algebraic geometry) applied to coding theory, Curves over finite and local fields, Arithmetic theory of algebraic function fields, Applications to coding theory and cryptography of arithmetic geometry Integral bases in a tower 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 fast algorithm; counting points on elliptic curves; finite fields of small characteristic Curves over finite and local fields, Number-theoretic algorithms; complexity, Finite ground fields in algebraic geometry An extension of Satoh's algorithm and its implementation | 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 QFT methods for algebraic number fields and fields of algebraic functions; factoring of polynomials; Nambu bracket; Zariski quantization Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Algebraic functions and function fields in algebraic geometry, Quantum field theory; related classical field theories, Relationships between algebraic curves and physics, Applications of Lie (super)algebras to physics, etc., Hamiltonian and Lagrangian mechanics, Geometry and quantization, symplectic methods Quantum field theories on an algebraic 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 algebraic torus; non-generate subvariety; heights, intersection numbers; Zariski-dense; resolution of singularities, Diophantine approximation G. Maurin, Équations multiplicatives sur les sous-variétés des tores, Int. Math. Res. Not. IMRN 23 (2011), 5259 -- 5366 (French). Arithmetic varieties and schemes; Arakelov theory; heights, Heights, Group varieties, Global theory and resolution of singularities (algebro-geometric aspects), Results involving abelian varieties Multiplicative equations over torus subvarieties | 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 Gersten's conjecture; characteristic \(p\); finiteness of \(p\)-torsion of zero-cycles; purity theorems for logarithmic Hodge-Witt sheaves; Cousin complex N. Suwa, ''A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves,'' \(K\)-Theory, vol. 9, iss. 3, pp. 245-271, 1995. \(p\)-adic cohomology, crystalline cohomology, Determinantal varieties, Finite ground fields in algebraic geometry, \(K\)-theory of schemes A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves | 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 algorithm for uniformizations in a neighborhood of a singular point; Newton polyhedra A. D. Bryuno and A. Soleev, ''Local uniformization of the branches of a space curve, and Newton polyhedra,'' Algebra i Analiz,3, No. 1, 67--101 (1991). Singularities of curves, local rings, Toric varieties, Newton polyhedra, Okounkov bodies, Curves in Euclidean and related spaces Local uniformization of branches of a space curve and Newton polyhedra | 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 semistable curve; moduli of curves; resolution of singularities; alteration; integral variety; monoidal transformations; semi-stable reduction theorem; multiplicity of intersection for two modules; Monsky-Washnitzer cohomology groups; monodromy actions on étale cohomology Berthelot, P., Altérations de variétés algébriques (d'après A.J. de jong), Séminaire Bourbaki, vol. 1995/96, Astérisque, 241, 273-311, (1997), Exp. No. 815, 5 Global theory and resolution of singularities (algebro-geometric aspects), Singularities in algebraic geometry, Families, moduli of curves (algebraic), \(p\)-adic cohomology, crystalline cohomology, Étale and other Grothendieck topologies and (co)homologies Alterations of algebraic varieties (after A. J. de Jong) | 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 arrangement of lines; combinatorial arrangement; containment problem for powers of ideals; Pappus theorem M. Lampa-Baczyńska; J. Szpond, From Pappus Theorem to parameter spaces of some extremal line point configurations and applications, Geom. Dedicata, 188, 103-121, (2017) Configurations and arrangements of linear subspaces, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Relations with arrangements of hyperplanes, Planar arrangements of lines and pseudolines (aspects of discrete geometry), Polynomial rings and ideals; rings of integer-valued polynomials From Pappus theorem to parameter spaces of some extremal line point configurations 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 Schottky uniformization of algebraic curves; real hyperelliptic \(M\)-curves; Schottky-Klein prime function; explicit conformal slit mapping Kleinian groups (aspects of compact Riemann surfaces and uniformization), Real-analytic and semi-analytic sets, Compact Riemann surfaces and uniformization Uniformizing real hyperelliptic \(M\)-curves using the Schottky-Klein prime function | 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 characteristic \(p\); Kodaira vanishing theorem; tight closure; system of parameters; local cohomology Huneke, C.; Smith, K. E.: Tight closure and the Kodaira vanishing theorem. J. reine angew. Math. 484, 127-152 (1997) Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Vanishing theorems in algebraic geometry, Integral closure of commutative rings and ideals, Local cohomology and commutative rings Tight closure and the Kodaira vanishing 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 Ext; satellites; duality theorem for the Galois cohomologies of commutative algebraic groups; Tamagawa numbers; Birch-Swinnerton-Dyer conjecture for abelian varieties Classical groups (algebro-geometric aspects), Galois cohomology, Global ground fields in algebraic geometry, Galois cohomology, Galois cohomology, Cohomology theory for linear algebraic groups Duality theorems in Galois cohomology of commutative algebraic 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 probabilistic algorithms; endomorphism ring of the Jacobian; computing of the field of definition; action of Frobenius; subgroups for prime powers; implementation of Eisenträger and Lauter's algorithm for computing Igusa class polynomials David Freeman and Kristin Lauter, Computing endomorphism rings of Jacobians of genus 2 curves over finite fields, Algebraic geometry and its applications, Ser. Number Theory Appl., vol. 5, World Sci. Publ., Hackensack, NJ, 2008, pp. 29 -- 66. Applications to coding theory and cryptography of arithmetic geometry, Finite ground fields in algebraic geometry, Jacobians, Prym varieties, Randomized algorithms Computing endomorphism rings of Jacobians of genus 2 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 semialgebraic set; ring of semialgebraic functions; extension of coefficients; evaluation homomorphisms; substitution theorem; weak continuous extension property; ring of bounded semialgebraic function; semialgebraic pseudo-compactification Fernando, JF, On the sustitution theorem for rings of semi-algebraic functions, J. Inst. Math. Jussieu, 14, 857-894, (2015) Semialgebraic sets and related spaces, Real-valued functions in general topology, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Chain conditions, finiteness conditions in commutative ring theory On the substitution theorem for rings of semialgebraic 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 KdV equation; sine-Gordon equation; two-zone solutions; addition theorem for theta-functions of two variables; Riemann matrix; Kadomtsev-Petviashvili equations Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions, KdV equations (Korteweg-de Vries equations), Theta functions and abelian varieties A direct method of construction of two-zone solutions of nonlinear 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 diophantine approximation; G-functions; algebraic functions; Hilbert's irreducibility theorem; height on abelian varieties Dèbes, P.: G-fonctions et théorème d'irréductibilité de Hilbert. Acta arith. 47 (1986) Hilbertian fields; Hilbert's irreducibility theorem, Transcendence theory of other special functions, Heights, Polynomials (irreducibility, etc.), Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry \(G\)-functions and Hilbert's irreducibility 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 Merkurev-Seislin theorem; Quillen-Lichtenbaum conjectures; algebraic K- theory of fields; Brauer-Severi varieties; Milnor K-groups; Bloch's group; Chow groups A. A. Suslin, ''Algebraic \(K\)-theory of fields,'' in Proceedings of the International Congress of Mathematicians, Vol. 1, 2, Providence, RI, 1987, pp. 222-244. \(K\)-theory of global fields, Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Grothendieck groups, \(K\)-theory and commutative rings, Parametrization (Chow and Hilbert schemes) Algebraic K-theory of 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 special divisor; special linear series on algebraic curves; Brill-Noether theory; Castelnuovo curves; theta function; Torelli theorem for curves E.~Arbarello, M.~Cornalba, P.A.~Griffiths, J.~Harris: {\em Geometry of Algebraic Curves}, Vol. I, Grundlehren der math. Wiss., 267, Springer-verlag, New York (1985). zbl 0559.14017; MR0770932 Curves in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Divisors, linear systems, invertible sheaves, Theta functions and abelian varieties, Picard groups, Special algebraic curves and curves of low genus Geometry of algebraic curves. Volume 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 Mordell-Lang conjecture for function fields; Drinfeld module; polynomial dynamics Ghioca, D., Tucker, T.J.: A dynamical version of the Mordell--Lang conjecture for the additive group. Compos. Math., to appear (arXiv:0704.1333 [math.NT]) Drinfel'd modules; higher-dimensional motives, etc., Subvarieties of abelian varieties, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets A dynamical version of the Mordell-Lang conjecture for the additive group | 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 Mordell-Weil group; procyclic extension of rational function field; elliptic curves over function fields Fastenberg, L., Mordell-Weil groups in procyclic extensions of a function field, Ph.D. Thesis, Yale University, 1996. Rational points, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Elliptic curves over global fields, Elliptic curves Mordell-Weil groups in procyclic extensions 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 polynomial ring in two variables; nontrivial embedding of affine; line into affine plane; logarithmic Kodaira dimension; characteristic p; coordinate line Richard Ganong, Kodaira dimension of embeddings of the line in the plane, J. Math. Kyoto Univ. 25 (1985), no. 4, 649 -- 657. Special algebraic curves and curves of low genus, Embeddings in algebraic geometry, Polynomial rings and ideals; rings of integer-valued polynomials, Special surfaces, Families, moduli of curves (algebraic) Kodaira dimension of embeddings of the line in the plane | 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 totally non-negative Grassmannians; amalgamation of positroid varieties; M-curves; KP hierarchy; real soliton and finite-gap solutions; positroid cells; planar bicolored networks in the disk; moves and reductions; Baker-Akhiezer function 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, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry, Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems, Plane and space curves, Relationships between algebraic curves and integrable systems Real regular KP divisors on \({\texttt{M}}\)-curves and totally non-negative Grassmannians | 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 zeta values; function fields Transcendence (general theory), Zeta functions and \(L\)-functions of number fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Report on transcendency in the 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 del Pezzo surfaces; fibrations; function fields of curves; rational points; intermediate Jacobians Hassett, B; Tschinkel, Y, Quartic del Pezzo surfaces over function fields of curves, Cent. Eur. J. Math., 12, 395-420, (2014) Arithmetic ground fields (finite, local, global) and families or fibrations, Families, moduli, classification: algebraic theory, Structure of families (Picard-Lefschetz, monodromy, etc.), Jacobians, Prym varieties, Rational points, Fano varieties Quartic del Pezzo surfaces over function fields of 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 Painlevé equations; Differential algebraic function fields; analytic subgroups; algebraic subgroups; birational automorphism group of a complex algebraic variety; Pfaffian differential equations over complex manifolds; algebraic differential equations N. N. Parfentiev, ''A review on the work by Prof. Schlesinger from Giessen,'' \textit{Izvestiya Fiz.-Mat. Obshchestva pri Imperat. Kazan. Universitete}, Ser. 2, \textbf{XVIII}, 4 (1912). Abstract differential equations, Birational automorphisms, Cremona group and generalizations, History of field theory, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies Birational automorphism groups and differential 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 cubic polynomials; Fatou index theorem; projective moduli space; parameterization in terms of multipliers K. Nishizawa and M. Fujimura, Moduli space of polynomial maps with degree four, Josai Information Sciences Researchers 9 (1997), 1--10. Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, Algebraic moduli problems, moduli of vector bundles, Affine geometry Projective moduli space of the polynomials: Cubic case. | 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 Ihara zeta function; prime cycle; determinant formula; functional equation; prime theorem; unramified covering; Galois theory; L-function; chaos theory A. Terras, \textit{Zeta functions of graphs: a stroll through the garden}, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge U.K. (2010). Research exposition (monographs, survey articles) pertaining to combinatorics, Graphs and abstract algebra (groups, rings, fields, etc.), Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Graphs and linear algebra (matrices, eigenvalues, etc.), \(\zeta (s)\) and \(L(s, \chi)\), Other Dirichlet series and zeta functions, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Zeta functions of graphs. A stroll through the garden | 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 non-reduced local moduli for algebraic surface of general type; hypersurfaces in a weighted projective space Catanese F. Everywhere non reduced moduli space. Invent Math, 1989, 98: 293--310 Hypersurfaces and algebraic geometry, Families, moduli, classification: algebraic theory, Algebraic moduli problems, moduli of vector bundles, Deformations of complex structures Everywhere non reduced moduli 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 curves over finite fields; gonality in positive characteristic; étale fundamental group; étale cohomology Cadoret, Anna; Tamagawa, Akio, Genus of abstract modular curves with level-\(\ell\) structures, J. reine angew. Math., (2016) Coverings of curves, fundamental group, Abelian varieties and schemes, Algebraic moduli of abelian varieties, classification Gonality of abstract modular curves 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 mixed Hodge structure; germ of holomorphic function; Grothendieck group; convolution theorem; non-degenerate with respect to Newton boundary; tame \(l\)-adic sheaves; composite singularities Singularities of surfaces or higher-dimensional varieties, Germs of analytic sets, local parametrization, Complex surface and hypersurface singularities Convolution theorem for non-degenerate maps and composite singularities | 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 category of rational maps; generalized Albanese varieties for smooth proper surfaces; characteristic \(p\) H. Önsiper, Generalized Albanese varieties for surfaces in characteristic p >0, Duke Math. J. 59 (1989), 359-364. Picard schemes, higher Jacobians, Finite ground fields in algebraic geometry, Rational and birational maps, Special surfaces Generalized Albanese varieties for surfaces in characteristic \(p>0\) | 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 finite fields; complex multiplication; construction of elliptic curves over finite fields; subgroup of large prime order Algebraic coding theory; cryptography (number-theoretic aspects), Elliptic curves over global fields, Applications to coding theory and cryptography of arithmetic geometry, Cryptography Rational groups of elliptic curves suitable for cryptography | 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 supercuspidal family of curves; pathology in positive characteristic; Frobenius; singular point Ichiro Shimada, On supercuspidal families of curves on a surface in positive characteristic, Math. Ann. 292 (1992), no. 4, 645 -- 669. Singularities of curves, local rings, Families, moduli of curves (algebraic), Finite ground fields in algebraic geometry On supercuspidal families of curves on a surface 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 level curve of a rational function on a smooth algebraic surface; points of indeterminacy; smooth prime curve; rational functions of \({\mathbb{C}}^*\)-type Kizuka T. , Rational functions of C \ast -type on the two-dimensional complex projective space , Tohoku Math. J. (2) 38 ( 1 ) ( 1986 ) 123 - 178 . Article | Zbl 0577.14021 Families, moduli of curves (analytic), Special surfaces, Holomorphic functions of several complex variables Rational functions of \({\mathbb{C}}^*\)-type on the two-dimensional complex projective space | 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 17th problem of Hilbert; Kochen operator; p-adically closed fields; isomorphism theorem; general embedding theorem; zero theorem of Hilbert Prestel, A.: Lectures on formally real fields. Lecture notes in mathematics 1093 (1983) Formally \(p\)-adic fields, Research exposition (monographs, survey articles) pertaining to field theory, Model theory of fields, Local ground fields in algebraic geometry, Valued fields, Polynomials in real and complex fields: factorization, Relevant commutative algebra Lectures on formally \(p\)-adic 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 characteristic \(p\); tame coverings; fundamental group; graph of groups; semi-stable curves; Belyi's theorem; semi-stable Kummerian coverings Saïdi, M., Rev\hat etements modérés et groupe fondamental de graphe de groupes, Compositio Math., 107 (1997), 319-338. Coverings of curves, fundamental group, Coverings in algebraic geometry, Finite ground fields in algebraic geometry Tame coverings and the fundamental group of graphs of 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 \(p\)-adic fields; differential character; abelian scheme; theorem of the kernel; arithmetic jet theory Buium, Alexandru, Differential characters of abelian varieties over \textit{p}-adic fields, Invent. Math., 122, 1, 309-340, (1995) Arithmetic ground fields for abelian varieties, Modules of differentials, Local ground fields in algebraic geometry Differential characters of abelian varieties over \(p\)-adic 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 invariants for singularities; Hironaka's characteristic polyhedra; resolution of singularities Singularities of surfaces or higher-dimensional varieties, Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Polytopes and polyhedra, Modifications; resolution of singularities (complex-analytic aspects) Invariance of Hironaka's characteristic polyhedron | 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 nested Artin approximation theorem; formal power series; problem of the commutation of two operation Étale and flat extensions; Henselization; Artin approximation, Power series rings, Local deformation theory, Artin approximation, etc. Linear nested Artin approximation theorem for algebraic power series | 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 prime geodesic theorem; arithmetic cocompact subgroup of \(\text{PSL} (2,\mathbb{R})\); Jacquet-Langlands correspondence; first eigenvalue of the Laplacian Koyama S. (1998). Prime geodesic theorem for arithmetic compact surfaces. Internat. Math. Res. Notices 8: 383--388 Spectral theory; trace formulas (e.g., that of Selberg), Arithmetic ground fields for surfaces or higher-dimensional varieties, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Estimates of eigenvalues in context of PDEs Prime geodesic theorem for arithmetic compact surfaces | 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; divisor class group of finite order; automorphisms; meromorphisms; addition theorems; structure of ring of meromorphisms; Riemann hypothesis Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Zur Theorie der abstrakten elliptischen Funktionenkörper. I: Die Struktur der Gruppe der Divisorenklassen endlicher Ordnung. II: Automorphismen und Meromorphismen. Das Additionsproblem. III: Die Struktur des Meromorphismenrings. Die Riemannsche Ver\-mutung. | 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; function fields; characteristic p; curves; abelian varieties Varieties over global fields, Arithmetic theory of algebraic function fields, Arithmetic varieties and schemes; Arakelov theory; heights, Global ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry Bounds for the number of rational points 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 approximation in local rings; polynomial equations; algebraic solutions; excellent Henselian discrete valuation rings; strong approximation theorems; theory of ultraproducts Becker J., Denef J., Lipshitz L., van den Dries L.: Ultraproducts and approximations in local rings. I. Invent. Math. 51(2), 189--203 (1979) Extension theory of commutative rings, Polynomials over commutative rings, Valuation rings, Henselian rings, Equations in general fields, Local deformation theory, Artin approximation, etc., Ultraproducts and related constructions, Local rings and semilocal rings Ultraproducts and approximation in local rings. 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 second Chern class; Yang-Mills fields; Donaldson theory; Atiyah-Jones conjecture; topological Euler characteristics of the moduli spaces Algebraic moduli problems, moduli of vector bundles, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), Characteristic classes and numbers in differential topology, Moduli problems for differential geometric structures, Twistor theory, double fibrations (complex-analytic aspects), Topological properties in algebraic geometry The Euler characteristics of \(SU(3)\)-instanton and moduli spaces over four sphere | 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 Teichmüller modular function fields; pro-\(l\) number field towers; moduli stack of smooth projective curves; stability; braid groups Nakamura, H.; Takao, N.; Ueno, R., Some stability properties of Teichmüller modular function fields with pro-\textit{} weight structures, Math. ann., 302, 197-213, (1995), MR 96h:14041 Arithmetic ground fields for curves, Coverings of curves, fundamental group, Families, moduli of curves (algebraic), Braid groups; Artin groups Some stability properties of Teichmüller modular function fields with pro-\(l\) weight structures | 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 abelian varieties; algebraic independence; analog of Lindemann-Weierstrass theorem; Weierstrass elliptic function; complex multiplication; zero lemmas P. Philippon, Variétés abéliennes et indépendance algébrique. II. Un analogue abélien du théorème de Lindemann-Weierstraß, Invent. Math. 72 (1983), no. 3, 389 -- 405 (French). Algebraic independence; Gel'fond's method, Results involving abelian varieties, Arithmetic ground fields for abelian varieties Abelian varieties and algebraic independence. II: An abelian analogue of the Lindemann-Weierstrass 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 towers of function fields; rational points; finite fields; hypergeometric functions; Deuring's polynomial Hasegawa, On asymptotically optimal towers over quadratic fields related to Gauss hypergeometric functions, Int. J. Number Theory 6 pp 989-- (2010) Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic coding theory; cryptography (number-theoretic aspects), Finite ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Classical hypergeometric functions, \({}_2F_1\) On asymptotically optimal towers over quadratic fields related to Gauss hypergeometric 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 function fields; irreducible polynomials; hyperelliptic curves; derivatives of \(L\)-functions; moments of \(L\)-functions; quadratic Dirichlet \(L\)-functions; random matrix theory Zeta and \(L\)-functions in characteristic \(p\), \(\zeta (s)\) and \(L(s, \chi)\), Curves over finite and local fields, Relations with random matrices, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Mean values of derivatives of \(L\)-functions in function fields. III | 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 surface singularities; resolution of singularities; invariants for singularities; Hironaka's characteristic polyhedra Research exposition (monographs, survey articles) pertaining to algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Singularities of surfaces or higher-dimensional varieties Desingularization: invariants and strategy. Application to dimension 2. With contributions by Bernd Schober | 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 torsor; moduli space of Higgs bundle; determinant of the cohomology of coherent sheaves on a curve; theorem of the cube; characteristic variety; theta-functions; semistable pairs; moduli stack; abelianisation; connection Faltings, Gerd, Stable {\(G\)}-bundles and projective connections, Journal of Algebraic Geometry, 2, 3, 507-568, (1993) Families, moduli of curves (algebraic), Vector bundles on curves and their moduli, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) Stable \(G\)-bundles and projective connections | 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 existence of a non-singular model for a variety; characteristic zero F.A. Bogomolov and T. Pantev: ''Weak Hironaka Theorem'', Math. Res. Let., Vol. 3, (1996), pp. 299--307. Minimal model program (Mori theory, extremal rays) Weak Hironaka 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 local fields; irreducible algebraic varieties; rationality problem for group varieties; semisimple algebraic groups; almost simple algebraic groups; number fields; global function fields; Tits indices Linear algebraic groups over arbitrary fields, Rational and unirational varieties, Group varieties, Rational points, Local ground fields in algebraic geometry On the problem of rational group 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 level curve of a rational function on a smooth algebraic surface; points of indeterminacy; smooth prime curve; rational functions of; \({\mathbb{C}}^*\)-type Kizuka, T.: Rational functions of ?*-type on the two-dimensional complex projective space. Tôhoku Math. J. 38, 123-178 (1986) Families, moduli of curves (analytic), Special surfaces, Holomorphic functions of several complex variables Rational functions of \({\mathbb{C}}^*\)-type on the two-dimensional complex projective space | 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; Bombieri-lang conjecture; varieties of general type Rational points, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Rational points of varieties with ample cotangent bundle 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; \(u\)-invariant; power series fields; function fields of curves; orderings of fields; patching of fields Scheiderer, Claus: The u-invariant of one-dimensional function fields over real power series fields, Arch. math. (Basel) 93, No. 3, 245-251 (2009) Algebraic theory of quadratic forms; Witt groups and rings, Quadratic forms over general fields, Algebraic functions and function fields in algebraic geometry The \(u\)-invariant of one-dimensional function fields over real power series 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 positive characteristic; uniform approximation of ideals; regular variety; Abhyankar valuation; test ideals; Frobenius morphism; Noetherian domain; graded system Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Valuations and their generalizations for commutative rings, Singularities in algebraic geometry, Valuation rings, Positive characteristic ground fields in algebraic geometry Uniform approximation of Abhyankar valuation ideals in function fields of prime 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 traces of Hecke operators; modular curves over a finite field; elliptic curves over a finite field; Petersson formula for newforms; Tsfasman-Vlăduţ-Zink theorem Hecke-Petersson operators, differential operators (one variable), Holomorphic modular forms of integral weight, Spectral theory; trace formulas (e.g., that of Selberg), Curves over finite and local fields, Finite ground fields in algebraic geometry Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite 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 Mordell conjecture; product theorem; Roth's lemma; diophantine approximation theory Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Rational points, Diophantine approximation, transcendental number theory, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory The product 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 representations of non-negative polynomials; degree bounds; optimization; quadratic modules; preorderings; local minima; global minima; Schmuedgen's theorem; first order theory of real closed fields; ultrafilters; gradient ideal; sums of squares relaxations M. Marshall, \textit{Representations of non-negative polynomials, degree bounds and applications to optimization,} Canad. J. Math., 61 (2009), pp. 205--221. Real algebra, Semidefinite programming, Computational aspects and applications of commutative rings, Semialgebraic sets and related spaces Representations of non-negative polynomials, degree bounds and applications to optimization | 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 class numbers; function fields; mean values of \(L\)-functions Andrade, J. C., A note on the mean value of \textit{L}-functions in function fields, Int. J. Number Theory, 8, 7, 1725-1740, (2012) Class numbers, class groups, discriminants, Arithmetic theory of algebraic function fields, Curves over finite and local fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) A note on the mean value of \(L\)-functions in 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; Riemann-Roch theorem Witt, E.: Riemann--Rochscher Satz und {\(\zeta\)}-Funktion im Hyperkomplexen. Math. Ann. 110, 12--28 (1934) Riemann-Roch theorems, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Riemann-Rochscher Satz und \(Z\)-Funktion im Hyperkomplexen | 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 functional equation for L-function; derivative of L-function; Birch and Swinnerton-Dyer conjecture; Iwasawa L-functions for abelian varieties with multiplicative reductions; p-adic height pairing John W. Jones, Iwasawa \?-functions for multiplicative abelian varieties, Duke Math. J. 59 (1989), no. 2, 399 -- 420. Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Algebraic theory of abelian varieties, Arithmetic varieties and schemes; Arakelov theory; heights, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture Iwasawa L-functions for multiplicative abelian 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 public key; discrete logarithm; finite abelian groups; cryptosystems; jacobians of hyperelliptic curves; finite fields; groups of almost prime order N. Koblitz, Hyperelliptic cryptosystems, J. Cryptology 1 (1989), no. 3, 139-150. Cryptography, Jacobians, Prym varieties, Finite ground fields in algebraic geometry Hyperelliptic cryptosystems | 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 variation of Hodge structures; Kähler hyperbolic manifold; Hermitian symmetric spaces of noncompact type; harmonic bundles; Kähler hyperbolicity; homogeneous holomorphic vector bundles; Lefschetz-Gromov vanishing theorem; Arakelov type inequalities; Chern classes; Gauss-Manin connection; formula of Kostant; scalar curvature for a griffiths period map; hyperrigidity 14. P. Eyssidieux, Kähler hyperbolicity and variations of Hodge structures, in New Trends in Algebraic Geometry, London Mathematical Society Lecture Note Series, Vol. 264 (Cambridge University Press, Cambridge, 1999), pp. 71-92. genRefLink(16, 'S0129167X1550113XBIB014', '10.1017%252FCBO9780511721540.005'); Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Variation of Hodge structures (algebro-geometric aspects), Vanishing theorems Kähler hyperbolicity and variations of Hodge structures | 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 construction; curves over finite fields; characteristic 2; supersingular curves; coding theory; generalized Hamming weights; odd characteristics; number of parameters G. VAN DER GEER - M. VAN DER VLUGT, On the existence of supersingular curves of given genus, J. Reine Angew. Math., 458 (1995), pp. 53-61. Zbl0819.11022 MR1310953 Curves over finite and local fields, Arithmetic ground fields for curves, Finite ground fields in algebraic geometry On the existence of supersingular curves of given genus | 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 tight closure; multiplier ideals; characteristic \(p\); prime characteristic; F-rationality; Briançon-Skoda theorem; test ideals HY N.~Hara and K.-i.~Yoshida, A generalization of tight closure and multiplier ideals, Trans. Amer. Math. Soc. \textbf 355 (2003), 3143--3174. Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Singularities in algebraic geometry, Integral closure of commutative rings and ideals A generalization of tight closure and multiplier ideals | 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 of function fields; singular points; rational function fields. Automorphisms of curves, Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry A relation between Galois automorphism and curve singularity | 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 n-valued formal groups; formal group in cobordism; 2n-periodic K-theory; Adams projectors; three-valued formal group of cobordism; characteristic classes of tensor products of complex n-plane bundles; representation of the Weyl group of a compact connected Lie group Bukhshtaber, V. M.; Kholodov, A. N.: Topological construction connected with many-valued formal groups. Math. USSR-izv. 20, 1-25 (1983) Bordism and cobordism theories and formal group laws in algebraic topology, Formal groups, \(p\)-divisible groups, Semisimple Lie groups and their representations, Topological \(K\)-theory Topological constructions connected with many-valued formal 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 logarithmic vanishing theorem; boundedness for families of canonically polarized varieties; rational Gorenstein singularities Kovács S. J., Comp. Math. 131 pp 291-- (2002) Vanishing theorems in algebraic geometry, Singularities in algebraic geometry Logarithmic vanishing theorems and Arakelov-Parshin boundedness for singular 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 rank of abelian variety; function fields; elliptic curve Pacheco, A.: The rank of abelian varieties over function fields. Manuscripta Math. 118, 361--381 (2005) Abelian varieties of dimension \(> 1\), Rational points, Arithmetic ground fields for curves, Arithmetic ground fields for abelian varieties On the rank of abelian 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 deformations in subscheme; comparison theorem; deformation of a family of coherent sheaves Formal methods and deformations in algebraic geometry, Parametrization (Chow and Hilbert schemes) A note on deformations of coherent sheaves | 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 abelian modular functions; algebraic surfaces; arithmetic groups; automorphic forms; automorphic functions; automorphic L-functions; bounded homogeneous domains; cuspidal automorphic representations; discrete groups; distinguished representations; distribution of prime numbers; Euler subgroups; functions of several complex variables; generalized Ramanujan conjecture for (quasi)-split groups Piatetski-Shapiro, I.: Selected works of ilya piatetski-shapiro, (2000) Collected or selected works; reprintings or translations of classics, History of number theory, History of algebraic geometry, History of topological groups, History of harmonic analysis on Euclidean spaces Selected works of Ilya Piatetski-Shapiro. Edited by James Cogdell, Simon Gindikin and Peter Sarnak | 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 cohomology of complement; arrangements of subspaces and of spheres in affine space; spherical and projective subspace arrangements; homology of the arrangement; homotopy direct limit; homotopy comparison results for diagrams of spaces 17.G. Ziegler, R. Živaljević, Homotopy types of subspace arrangements via diagrams of spaces. Math. Ann. 295, 527-548 (1993) Classification of homotopy type, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Homology and cohomology theories in algebraic topology, Complete intersections Homotopy types of subspace arrangements via diagrams of 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 integral points; function fields; Diophantine equations Lattice points in specified regions, Algebraic functions and function fields in algebraic geometry On the Bombieri-Pila method 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 elliptic curves over a local field; algorithm for the reduction type of a minimal model; characteristic 2; characteristic 3; Weierstrass model; 315 Papadopoulos, Ioannis, Sur la classification de Néron des courbes elliptiques en caractéristique résiduelle \(2\) et \(3\), J. Number Theory, 44, 2, 119-152, (1993) Elliptic curves, Local ground fields in algebraic geometry, Computational aspects of algebraic curves, Elliptic curves over local fields On Néron's classification of elliptic curves of residue characteristics 2 and 3 | 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 ordered groups; convex subgroups; valuation rings; Henselian domain; schemes of finite presentation; ultraproducts; Greenberg's strong approximation theorem; closed image theorem; infinitesimal Hasse principle; closed image map Moret-Bailly, L.: An extension of Greenberg's theorem to general valuation rings, Manuscripta math. 139, 153-166 (2012) Étale and flat extensions; Henselization; Artin approximation, Valuation rings, Ultraproducts and field theory, Other nonalgebraically closed ground fields in algebraic geometry An extension of Greenberg's theorem to general valuation rings | 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 curves; algebraic function fields; maximal curves; maximal function fields; automorphisms of function fields Güneri, C.; Özdemir, M.; Stichtenoth, H., The automorphism group of the generalized giulietti-korchmáros function field, \textit{Adv. Geom.}, 13, 369-380, (2013) Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The automorphism group of the generalized Giulietti-Korchmáros 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 Ihara zeta-functions; primes in graphs; graph theory prime-number theorem Graphs and abstract algebra (groups, rings, fields, etc.), Enumeration in graph theory, Paths and cycles, Graphs and linear algebra (matrices, eigenvalues, etc.), Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, \(\zeta (s)\) and \(L(s, \chi)\), Other Dirichlet series and zeta functions, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) A generalization of the graph theory prime-number theorem of a finite graph | 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 exceptional divisors; Euler characteristic; embedded resolution of zero set; local zeta function; topological zeta function Global theory and resolution of singularities (algebro-geometric aspects), Topological properties in algebraic geometry, Zeta functions and \(L\)-functions, Divisors, linear systems, invertible sheaves On Euler characteristics associated to exceptional divisors | 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 textbook; partially ordered sets; Zorn's lemma; number theory; fields; rings; abelian groups; polynomials; field extension; formal power series; polynomial rings; finite fields; power series; rational function; Bernoulli numbers; Puiseux series; Laurent series; ideals; quotient rings; factorization; Noetherian rings; prime ideals; principal ideal domains; cyclic groups; homomorphism; group action; quotient group; symmetric group; semidirect product; Sylow group; modules; free modules; commutative ring; Smith normal form; elementary divisor; Jordan form; Hermitian space; projective space; bilinear form; symplectic space; quadratic form; Kähler triples; quaternions; spinors Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory Algebra I. Textbook for students of mathematics. Translated from the Russian | 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 Brauer groups; indecomposable division algebras; noncrossed products; ramification; function fields of smooth curves; non-crossed product central division algebras; exponents; indices; periods; tensor products of central algebras E. Brussel, K. McKinnie, and E. Tengan, Indecomposable and noncrossed product division algebras over function fields of smooth \?-adic curves, Adv. Math. 226 (2011), no. 5, 4316 -- 4337. Finite-dimensional division rings, Skew fields, division rings, Algebraic functions and function fields in algebraic geometry, Brauer groups (algebraic aspects) Indecomposable and noncrossed product division algebras over function fields of smooth \(p\)-adic 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 Mordell-Weil group; multidimensional function fields; Néron-Tate height; Mordell-Weil rank; Jacobian; independence of some rational points T. Shioda, Constructing curves with high rank via symmetry, Amer. J. Math., to appear. Algebraic functions and function fields in algebraic geometry, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields Constructing curves with high rank via symmetry | 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 Mordell-Lang conjecture; rational points; torsion points; algebraically closed field; semi-Abelian variety; differentially closed field; group subvarieties; separably closed fields; Hrushovski-Zil'ber Dichotomy Theorem; diophantine geometry; Zariski geometry Manin, Y.I.: Letter to the editors: ''Rational points on algebraic curves over function fields'' [Izv. Akad. Nauk SSSR Ser. Mat. 27 (1963), 1397-1442; MR0157971 (28 #1199)], Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), no. 2, 447-448 (Russian); English transl., Math. USSR-Izv. 34 (1990), no. 2, 465-466 Model-theoretic algebra, Rational points, Abelian varieties of dimension \(> 1\), Classification theory, stability, and related concepts in model theory The Mordell-Lang 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 circle method; function fields; diagonal hypersurfaces; Vinogrador's mean value theorem; Waring's problem Zhao, X.: Asymptotic estimates for rational spaces on hypersurfaces in function fields, Proc. lond. Math. soc. (3) 104, 287-322 (2012) Applications of the Hardy-Littlewood method, Varieties over global fields, Arithmetic theory of polynomial rings over finite fields, Waring's problem and variants, Global ground fields in algebraic geometry, Estimates on exponential sums Asymptotic estimates for rational spaces on hypersurfaces in 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 free energy; Euler characteristic of the moduli space; punctured compact Riemann surfaces; Penner's connected generating function N. Chair, Rev. Math. Phys. 3 pp 285-- (1991) Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic) The (orbifold) Euler characteristic of the moduli space of curves and the continuum limit of Penner's connected generating function | 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 global function fields; rational places; curves over finite fields; lower bound for \(A(2), A(3)\); class field towers; Drinfel'd-Vlădut bound Angles B., Maire C.: A note on tamely ramified towers of global function fields. Finite Field Appl. \textbf{8}, 207-215 (2002). Curves over finite and local fields, Arithmetic theory of algebraic function fields, Class field theory, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Rational points, Arithmetic ground fields for curves A note on tamely ramified towers of global 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 effective geometric Bogomolov conjecture; curves of genus 3 over function fields; self-intersection of the relative dualizing sheaf; admissible constants of the metrized dual graph K. Yamaki, Geometric Bogomolov's conjecture for curves of genus 3 over function fields, J. Math. Kyoto Univ. 42 (2002), 57-81. Varieties over global fields, Global ground fields in algebraic geometry Geometric Bogomolov's conjecture for curves of genus 3 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 division algebras; cyclic algebras; ramifications; étale cohomology; function fields of surfaces; affine schemes; Brauer groups; central algebras; fields of fractions; cyclic Galois extensions Colliot-Thélène, J.-L.: Conjectures de type local-global sur image des groupes de Chow dans la cohomologie étale. In: Algebraic K-theory (Seattle, WA, 1997), Proceedings of Symposia in Pure Mathematics, vol. 67, pp. 1-12. Amer. Math. Soc., Providence (1999) Finite-dimensional division rings, Étale and other Grothendieck topologies and (co)homologies, Brauer groups of schemes, Brauer groups (algebraic aspects) Division algebras over surfaces. | 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 Euler's Diophantine equation; \(K3\) surface; elliptic curve over a function field; rank of an elliptic curve; Picard number of a \(K3\) surface Ono, K; Trebat-Leder, S, The 1729 \(K3\) surface, Res. Number Theory, 2, 26, (2016) Rational points, Elliptic curves The 1729 \(K3\) 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 algebraic number fields; valuation theory; class field theory; Arakelov theory; zeta functions; \(L\)-series; algebraic curves over arithmetic ground fields; arithmetic algebraic geometry; geometric approach to algebraic orders; singular algebraic curves; Grothendieck-Riemann-Roch theory for algebraic schemes; Hecke's \(L\)-series; Artin theory of \(L\)-series; selected exercises Neukirch, Jürgen, Algebraische zahlentheorie, (1992), Springer-Verlag Berlin, (in German) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic problems in algebraic geometry; Diophantine geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Arithmetic algebraic geometry (Diophantine geometry), Algebraic number theory: global fields, Algebraic number theory: local fields, Curves in algebraic geometry, Hurwitz and Lerch zeta functions Algebraic number 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 unique factorization; congruence; quadratic reciprocity; quadratic Gauss sums; Jacobi sums; cubic and biquadratic reciprocity; equations over finite fields; zeta functions; quadratic and cyclotomic fields; Stickelberger relation; Eisenstein reciprocity law; Bernoulli numbers; Dirichlet L-functions; Mordell-Weil theorem for elliptic curves; Mordell conjecture; Taniyama-Weil conjecture; Fermat's last theorem; Birch- Swinnerton-Dyer conjecture; Gauss' class number conjecture K. Ireland and M. Rosen, \textit{A Classical Introduction to Modern Number Theory}, (2nd ed.), Springer, 1990. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Elementary number theory, Arithmetic algebraic geometry (Diophantine geometry), Multiplicative number theory, Algebraic number theory: global fields, Finite fields and commutative rings (number-theoretic aspects), Diophantine equations, Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Higher degree equations; Fermat's equation, Elliptic curves A classical introduction to modern number 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 \(L\)-values in positive characteristic; log-algebraic theorem; generalized Drinfeld modules; Tate algebras; Herbrand-Ribet theorem; Carlitz module; class modules, Bernoulli-Carlitz fractions Anglès, B.; Pellarin, F.; Tavares Ribeiro, F., Arithmetic of positive characteristic \textit{L}-series values in Tate algebras. With an appendix by F. Demeslay, Compos. Math., 152, 1, 1-61, (2016) Modular forms associated to Drinfel'd modules, Formal groups, \(p\)-divisible groups, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Global ground fields in algebraic geometry Arithmetic of positive characteristic \(L\)-series values in Tate algebras | 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 in finite characteristic; six exponentials theorem Arithmetic theory of algebraic function fields, Transcendence (general theory), Formal groups, \(p\)-divisible groups, Algebraic functions and function fields in algebraic geometry A six exponentials theorem in finite 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 towers of function fields; asymptotically good towers; Drinfeld-Vladut bound; Artin-Schreier extension; long algebraic-geometric codes with good parameters García, A.; Stichtenoth, H., On the asymptotic behaviour of some towers of function fields over finite fields, J. Number Theory, 61, 248-273, (1996) Arithmetic theory of algebraic function fields, Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic ground fields for curves, Geometric methods (including applications of algebraic geometry) applied to coding theory On the asymptotic behaviour of some towers of function fields 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 multisymmetric polynomials; reflection groups; polynomial invariant; second fundamental theorem; ideal of relations; trace identities 10.Domokos, M.: Vector invariants of a class of pseudo-reflection groups and multisymmetric syzygies. J. Lie Theory 19, 507-525 (2009) Actions of groups on commutative rings; invariant theory, Group actions on varieties or schemes (quotients), Representation theory for linear algebraic groups Vector invariants of a class of pseudoreflection groups and multisymmetric 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 algebraic deformation; rigidity theorem for homogeneous-rational manifolds; morphism of complex algebraic varieties Algebraic moduli problems, moduli of vector bundles, Rational and unirational varieties, Deformations of complex structures, Homogeneous spaces and generalizations, Formal methods and deformations in algebraic geometry A rigidity theorem for homogeneous rational manifolds of rank 1 | 0 |
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