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higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Kerr, M.: Exterior products of zero-cycles. J. Reine Angew. Math. 600, 1--23 (2006) Algebraic cycles, (Equivariant) Chow groups and rings; motives, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Exterior products of zero-cycles | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves abelian variety without complex multiplication; Hodge conjecture; Mumford-Tate conjecture; Tate conjecture on algebraic cycles S. G. Tankeev, ''Algebraic cycles on an Abelian variety with no complex multiplication'',Izv. Ross. Akad. Nauk, Ser. Mat. 58, No. 3, 103--126 (1994). Transcendental methods, Hodge theory (algebro-geometric aspects), Complex multiplication and abelian varieties, Algebraic cycles Algebraic cycles on an abelian variety without complex multiplication | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves semistable Higgs sheaves; elliptic surfaces; curve semistability Vector bundles on curves and their moduli, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Vector bundles on surfaces and higher-dimensional varieties, and their moduli Semistable Higgs bundles on elliptic surfaces | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves strong Weil curve; Manin constant; Néron model functor; Manin's conjecture; semi-stable elliptic curves Abbes, Ahmed; Ullmo, Emmanuel, À propos de la conjecture de Manin pour les courbes elliptiques modulaires, Compositio Math., 103, 3, 269-286, (1996) Elliptic curves over global fields, Elliptic curves, Modular and Shimura varieties On the Manin conjecture for modular elliptic curves | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves (Equivariant) Chow groups and rings; motives, Homogeneous spaces and generalizations, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Group actions on varieties or schemes (quotients) Addendum to the paper: The Chow rings of \(G_{2}\) and \(\text{Spin}(7)\) | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves \(K3\) surfaces; explicit unirational moduli spaces; Gushel-Mukai fourfolds \(K3\) surfaces and Enriques surfaces, \(4\)-folds, Computational aspects of algebraic surfaces Explicit constructions of \(K3\) surfaces and unirational Noether-Lefschetz divisors | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves corank; finiteness; \(p\)-primary torsion part; Chow group of zero-cycles; Fermat quartic surface; Selmer groups; conjectures of Beilinson and Bloch-Kato Varieties over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, (Equivariant) Chow groups and rings; motives, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Global ground fields in algebraic geometry Selmer groups and zero-cycles on the Fermat quartic surface | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves quadric hypersurfaces; Chow group; stabilization conjecture Parametrization (Chow and Hilbert schemes), Hypersurfaces and algebraic geometry, (Equivariant) Chow groups and rings; motives, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) Chow groups of quadrics and the stabilization conjecture | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Selmer group; Bloch-Kato conjecture; elliptic curve Elliptic curves over global fields, Galois cohomology, Modular and Shimura varieties Bounding cubic-triple product Selmer groups of elliptic curves | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Runge's method; integral points on varieties; abelian varieties Varieties over global fields, Abelian varieties of dimension \(> 1\), Rational points, Modular and Shimura varieties A tubular variant of Runge's method in all dimensions, with applications to integral points on Siegel modular varieties | 0 |
higher Chow cycle; product of two elliptic curves; product of three elliptic curves; Deligne cohomology Gordon B. and Lewis J.\ D., Indecomposable higher Chow cycles on products of elliptic curves, J. Alg. Geom. 8 (1999), 543-567. (Equivariant) Chow groups and rings; motives, Elliptic curves, Parametrization (Chow and Hilbert schemes), Algebraic cycles Indecomposable higher Chow cycles on products of elliptic curves Qiu, D.; Zhang, X., Explicit classification for torsion cyclic subgroups of rational points with even orders of elliptic curves, Chinese Sci. Bull., 44, 1951-1953, (1999) Elliptic curves, Elliptic curves over global fields Explicit classification for torsion cyclic subgroups of rational points with even orders of elliptic curves | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Diophantine approximation; rational points on algebraic varieties; arithmetic algebraic geometry; Roth's theorem; nonvanishing lemma for polynomials in several variables; Roth's lemma; Dyson's lemma; Mordell conjecture; Faltings' theorem; finiteness of rational points; algebraic curve of genus greater than one; Vojta's generalization of Dyson's lemma; products of curves of arbitrary genus; Lang conjecture; Subspace Theorem; lower bound for the rational approximation to a hyperplane Results involving abelian varieties, Varieties over global fields, Abelian varieties of dimension \(> 1\), Rational points Diophantine approximation on algebraic varieties | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic variety; \(abc\)-conjecture; finiteness theorem for \(S\)-unit points of a diophantine equation; Nevanlinna-Cartan theory over function fields Varieties over global fields, Rational points, Diophantine approximation, transcendental number theory, Nevanlinna theory; growth estimates; other inequalities of several complex variables Value distribution theory over function fields and a diophantine equation | 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 equations of genus zero and one; function field; algorithms; effective determination; diophantine equations in two unknowns; Thue equations; hyperelliptic equations; fundamental inequality; fields of positive characteristic; explicit bounds; solutions in rational functions; superelliptic equations R. C. Mason, \textit{Diophantine Equations over Function Fields.} London Mathematical Society Lecture Note Series, Vol. 96. Cambridge Univ. Press, Cambridge, 1984. \(p\)-adic and power series fields, Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic theory of algebraic function fields, Exponential Diophantine equations, Diophantine equations, Approximation to algebraic numbers, Higher degree equations; Fermat's equation, Rational points Diophantine equations 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 ABC conjecture; the error term in the ABC conjecture; radicalized Vojta height inequality; Diophantine approximation; Roth's theorem; type of an algebraic number; Mordell's conjecture; effective Mordell van Frankenhuijsen, Machiel, \(ABC\) implies the radicalized Vojta height inequality for curves, J. Number Theory, 127, 2, 292-300, (2007) Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Counting solutions of Diophantine equations, Diophantine inequalities, Arithmetic varieties and schemes; Arakelov theory; heights ABC implies the radicalized Vojta height inequality for 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 logarithmic height function; Fermat Last Theorem; finiteness conjectures in Diophantine geometry; degenerate set of integral points; analogy between the theory of Diophantine approximation in number theory and value distribution theory; Nevanlinna theory; local height function; abc- conjecture; size of integral points on elliptic curves P. Vojta, Diophantine Approximations and Value Distribution Theory, Lecture Notes in Math. 1239, Springer, Berlin, 1987. Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Research exposition (monographs, survey articles) pertaining to number theory, Value distribution theory in higher dimensions, Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces, Arithmetic algebraic geometry (Diophantine geometry), Rational points, Arithmetic ground fields for curves, Global ground fields in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties Diophantine approximations and value distribution 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 isotriviality; effective Mordell; semiabelian variety; positive characteristic; survey of diophantine geometry; bounding the heights of rational points on curves over function fields; semiabelian varieties; Roth's theorem Voloch, José Felipe, Diophantine geometry in characteristic \(p\): a survey.Arithmetic geometry, Cortona, 1994, Sympos. Math., XXXVII, 260-278, (1997), Cambridge Univ. Press, Cambridge Rational points, Local ground fields in algebraic geometry, Arithmetic algebraic geometry (Diophantine geometry), Arithmetic ground fields for curves Diophantine geometry in characteristic \(p\): A survey | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic diophantine equations; Siegel's theorem; integral points on affine curves; function-fields of characteristic zero José Felipe Voloch, Siegel's theorem for complex function fields, Proc. Amer. Math. Soc. 121 (1994), no. 4, 1307 -- 1308. Elliptic curves over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry Siegel's theorem for complex 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 rational points; inseparable extensions of function field; Mordell conjecture for number fields; genus drop; prime characteristic; non-conservative curves Voloch, J. F.: A Diophantine problem on algebraic curves over function fields of positive characteristic. Bull. soc. Math. France 119, 121-126 (1991) Rational points, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry, Curves in algebraic geometry A Diophantine problem on algebraic curves over function fields of 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 diophantine equations; analogue of Thue equation; polynomial ring; diophantine approximation in fields of series; rational function solutions; first order algebraic differential equations \(p\)-adic and power series fields, Higher degree equations; Fermat's equation, Approximation in non-Archimedean valuations, Global ground fields in algebraic geometry Polynomial solutions of \(F(x,y)=z^n\). | 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 Schmidt's Subspace theorem; function field; diophantine approximation; Chow form; Hilbert weight; degree of contact M. Ru and J. T.-Y. Wang, An effective Schmidt's subspace theorem for projective varieties over function fields, Int. Math. Res. Not. IMRN 3 (2012), 651--684. Schmidt Subspace Theorem and applications, Arithmetic varieties and schemes; Arakelov theory; heights, Value distribution theory in higher dimensions An effective Schmidt's subspace theorem for projective 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 Stickelberger element; Galois module structure; Gras conjecture; Drinfeld modules; Herbrand criterion; crystalline cohomology; zeta-functions for function fields over finite fields; L-series; Teichmüller character; characteristic polynomial of the Frobenius; p-adic Tate-module; p-class groups; cyclotomic function fields; 1-unit root Goss, D., Sinnott, W.: Class-groups of function fields. Duke Math. J. 52(2), 507--516 (1985). http://www.ams.org/mathscinet-getitem?mr=792185 Arithmetic theory of algebraic function fields, \(p\)-adic cohomology, crystalline cohomology, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Iwasawa theory Class-groups 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 Pierre de Fermat; René Descartes; Leonhard Euler; affine space; barycenter; real affine space; Pasch's theorem; Euclidean space; metric space; Gram-Schmidt process; approximation by the law of least squares; Fourier approximation; Hermitian space; projective space; duality principle; Fano's theorem; projective quadric; Pascal's theorem; Brianchon's theorem; topology of projective real spaces; algebraic plane curves; Bezout's theorem; Hessian curve; Cramer's paradox; group of a cubic; rational algebraic plane curve; Taylor's formula for polynomials in one or more variables; Eisenstein's criterion; Euler's formula; fundamental theorem of algebra; Sylvester's theorem Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry, General histories, source books, Linear incidence geometric structures with parallelism, Affine analytic geometry, Projective analytic geometry, Euclidean analytic geometry, Questions of classical algebraic geometry, Algebraic functions and function fields in algebraic geometry, Projective techniques in algebraic geometry An algebraic approach to geometry. Geometric trilogy II | 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 upper bounds for solutions of diophantine equations; Runge theorem; finiteness of number of solutions; Brauer-Siegel theorem; Baker-Coates theory; linear forms in logarithms of algebraic numbers; \(p\)-adic case; representation of numbers by binary forms; Thue equation; rational approximations to algebraic numbers; effective strengthening of Liouville inequality; solution of Thue equation in \(S\)-integers; non-Archimedean metrics; polynomial equation; Mordell equation; Catalan equation; size of ideal class group; small regulator; effective variants of Hilbert on irreducibility of polynomials; Abelian points on algebraic curves Sprindžuk, Vladimir G., Classical Diophantine Equations, Lecture Notes in Mathematics 1559, xii+228 pp., (1993), Springer-Verlag, Berlin Diophantine equations, Diophantine approximation, transcendental number theory, Research exposition (monographs, survey articles) pertaining to number theory, Polynomials (irreducibility, etc.), Class numbers, class groups, discriminants, Arithmetic problems in algebraic geometry; Diophantine geometry Classical diophantine 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 Mordell conjecture for function fields; theorem of the kernel doi:10.2307/2374831 Rational points, Arithmetic theory of algebraic function fields, History of algebraic geometry A note on Manin's theorem of the kernel | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic fields of large transcendence degree; algebraic independence; zero lemmas; zero estimate for group varieties; primary ideal; polynomial rings; algebraic subgroups of products of elliptic curves; effective version of Hilbert's Nullstellensatz; Kolchin theorem; Weierstrass elliptic function Masser, D. W.; Wüstholz, G., Fields of large transcendence degree generated by values of elliptic functions, Invent. Math., 72, 3, 407-464, (1983) Transcendence theory of elliptic and abelian functions, Varieties over global fields, Global ground fields in algebraic geometry Fields of large transcendence degree generated by values of elliptic 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 Roth theorem; Dyson lemma; polynomials in several variables; hypersurface; approximation point; positivity for direct images of dualizing sheaves; Kodaira type vanishing theorems of \({\mathbb{Q}}\)-divisors Approximation to algebraic numbers, Transcendental methods, Hodge theory (algebro-geometric aspects), Homogeneous approximation to one number Dyson's lemma for polynomials in several variables (and the theorem of Roth) | 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 \(G\)-functions; formal power series; linear differential equation; \(p\)- adic differential equations; Padé approximants; general introduction to \(p\)-adic analysis; Dwork's theorem; rationality of the zeta function of a hypersurface over a finite field; \(D\)-modules; Honda's theory of differential equations in finite characteristics; applications to Katz' theorem; Dwork-Robba theorem; Dwork's transfer principles; Chudnovsky's theorem; Dwork-Robba type estimates; growth of solutions at the boundary of a singular disk; nilpotent monodromy; diophantine nature of the exponents; equivalence of Bombieri's and Galochkin's conditions B. \textsc{Dwork}, G. \textsc{Gerotto} and F. \textsc{Sullivan}, \textit{An Introduction to G-Functions}, Annals of Mathematical Studies, vol.~133, Princeton University Press, Princeton, 1994. \(p\)-adic differential equations, Research exposition (monographs, survey articles) pertaining to field theory, Transcendence theory of other special functions, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Local ground fields in algebraic geometry, Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects), Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), Padé approximation An introduction to \(G\)-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 meromorphic functions; number field analogue of Nevanlinna's five-valued theorem counting multiplicities; uniqueness polynomials for complex meromorphic functions; non-Archimedean meromorphic functions; algebraic function fields Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, Research exposition (monographs, survey articles) pertaining to functions of a complex variable, Algebraic functions and function fields in algebraic geometry, Non-Archimedean function theory Uniqueness polynomials, unique range sets and other uniqueness theorems | 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 log Hodge de Rham spectral sequences in finite characteristic; log Kodaira vanishing theorem in finite characteristic; log weak Lefschetz conjecture for log crystalline cohomologies; quasi-F-split height; log deformation theory with relative Frobenius; lifts of log smooth integral schemes over \(\mathcal{W}_2\) \(p\)-adic cohomology, crystalline cohomology, de Rham cohomology and algebraic geometry, Calabi-Yau manifolds (algebro-geometric aspects) Degenerations of log Hodge de Rham spectral sequences, log Kodaira vanishing theorem in characteristic \(p>0\) and log weak Lefschetz conjecture for log crystalline cohomologies | 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 places of algebraic function fields; description of holomorphy ring of function fields; proof of Ax-Kochen-Ershov theorem; approximation theorems Kuhlmann, F. -V.; Prestel, A.: On places of algebraic function fields. J. reine angew. Math. 353, 181-195 (1984) General valuation theory for fields, Arithmetic theory of algebraic function fields, Model theory of fields, Transcendental field extensions, Real algebraic and real-analytic geometry, Model-theoretic algebra, Local ground fields in algebraic geometry Places of algebraic function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic polynomials in several variables; hypersurface; approximation point; positivity for direct images of dualizing sheaves; Kodaira type vanishing theorems of \({\mathbb{Q}}\)-divisors; Roth theorem; Dyson lemma Hélène Esnault and Eckart Viehweg, Dyson's lemma for polynomials in several variables (and the theorem of Roth), Invent. Math. 78 (1984), no. 3, 445 -- 490. Approximation to algebraic numbers, Transcendental methods, Hodge theory (algebro-geometric aspects), Homogeneous approximation to one number Dyson's lemma for polynomials in several variables (and the theorem of Roth) | 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 explicit formulae of prime number theory; Riemann zeta-function; Poisson summation formula; Riemann hypothesis; Hadamard product formula; zeros; prime number theorem; Lindelöf hypothesis; zeta-functions attached to curves over finite fields; approximate functional equation; large number of exercises Patterson, S.J. (1988). An Introduction to the Theory of the Riemann Zeta-Function. Cambridge Studies in Advanced Mathematics 14 . Cambridge: Cambridge Univ. Press. \(\zeta (s)\) and \(L(s, \chi)\), Research exposition (monographs, survey articles) pertaining to number theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry An introduction to the theory of the Riemann 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 prime characteristic; K-scheme; involutive distribution; integrable distributions; Zassenhaus algebra; Kronecker quiver; Frobenius theorem; algebra of truncated polynomials; TI-distributions; Lie algebra of Cartan type M. I. Kuznetsov, ''Distributions over a truncated polynomial algebra,'' Mat. Sb. 136(2), 187--205 (1988). [Sb. Math. 64 (1), 187--205 (1989). Modular Lie (super)algebras, Algebraic theory of abelian varieties, Representation theory of associative rings and algebras, Automorphisms, derivations, other operators for Lie algebras and super algebras Distributions over an algebra of truncated polynomials | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic arithmetic theorem of algebraic function fields; L-function of Galois covering of curves; function-field; characteristic polynomial of the Hasse-Witt matrix; generalised Hasse-Witt invariants Cyclotomic function fields (class groups, Bernoulli objects, etc.), 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), Galois theory Class groups and \(L\)-series of congruence 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 explicit formulae of prime number theory; Riemann zeta-function; Poisson summation formula; Riemann hypothesis; Hadamard product formula; zeros; prime number theorem; Lindelöf hypothesis; zeta-functions attached to curves over finite fields; approximate functional equation; large number of exercises Patterson, S. J., An introduction to the theory of the Riemann zeta-function, (1995), Cambridge University Press \(\zeta (s)\) and \(L(s, \chi)\), Research exposition (monographs, survey articles) pertaining to number theory, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Distribution of primes An introduction to the theory of the Riemann 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 Frobenius classes; volumes of tubes; semi-algebraic set; prime number theorem in algebraic number fields; Chebotarev's density theorem; equidistribution of prime ideals B. Z. Moroz, ''Equidistribution of Frobenius classes and the volumes of tubes,'' Acta Arith., 51, 269--276 (1988). Density theorems, Primes in congruence classes, Real algebraic and real-analytic geometry Equidistribution of Frobenius classes and the volumes of tubes | 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; extremal rays; Mori's structure theorem for threefolds; deformation theory of curves in smooth threefolds Kollár, Ann. Sci. Éc. Norm. Supér. (4) 24 pp 339-- (1991) \(3\)-folds, Formal methods and deformations in algebraic geometry Extremal rays on smooth threefolds | 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 Anderson-Thakur function; \(L\)-functions in positive characteristic; function fields of positive characteristic Bruno Anglès & Federico Pellarin , Functional identities for \(L\) -series values in positive characteristic , J. Number Theory 142 (2014), p. 223-251 Zeta and \(L\)-functions in characteristic \(p\), Modular forms associated to Drinfel'd modules, Formal groups, \(p\)-divisible groups Functional identities for \(L\)-series values 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 formal languages; algebraic geometry over finite fields; rationality of zeta function; zeta function; formal power series; cyclic language; minimal ideals in finite semigroups; characteristic series; cyclic recognizable language; traces of finite deterministic automata; sofic system; symbolic dynamics J. BERSTEL and C. REUTENAUER, Zeta functions of formal languages. Trans. Amer. Math. Soc., 1990, 321, pp. 533-546. Zbl0797.68092 MR998123 Formal languages and automata, Semigroups in automata theory, linguistics, etc., Exact enumeration problems, generating functions, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics, Algebraic theory of languages and automata Zeta functions of formal languages | 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 proof of the conjecture of Birch and Swinnerton-Dyer for an abelian variety over a function field; Hasse-Weil zeta-function; Tate-Shafarevich group; prime characteristic Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Arithmetic ground fields for abelian varieties On the Birch and Swinnerton-Dyer conjecture for abelian varieties over function fields 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 arithmetic of elliptic curves; determining the group of rational points; Mordell-Weil theorem; Birch and Swinnerton-Dyer conjecture; Hasse-Weil L-series; effective determination of all imaginary quadratic fields with given class number; Iwasawa theory; main conjecture for elliptic curves; descent method Coates, J.: Elliptic curves and Iwasawa theory. In: Modular forms. Rankin, R.A. (ed.), pp. 51-73. Chichester: Ellis Horwood Ltd (1984) Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Iwasawa theory, Research exposition (monographs, survey articles) pertaining to number theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Elliptic curves and Iwasawa 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 finite fields; character sums; Weil conjectures; Riemann-Roch theorem; points on curves over finite fields; zeta-functions; \(L\)-functions; idele class characters; modular forms; automorphic representations; Ramanujan graphs; Alon-Boppana theorem; regular graphs; Riemann hypothesis for zeta functions of curves over finite fields; exponential sums; Cayley graphs; finite upper half plane graphs; valuations of function fields; projective curve; Hecke operators; automorphic representations of quaternion groups; expander; simple random walk; spectral theory of graphs Li, W. -C. Winnie: Number theory with applications. Series of university mathematics 7 (1996) Research exposition (monographs, survey articles) pertaining to number theory, Modular and automorphic functions, Graph theory, Arithmetic theory of algebraic function fields, Curves over finite and local fields, Representation-theoretic methods; automorphic representations over local and global fields, Holomorphic modular forms of integral weight, Estimates on exponential sums, Exponential sums, Adèle rings and groups, Representations of Lie and linear algebraic groups over global fields and adèle rings, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Number theory with 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 Algebraic curves; algebraic function fields; automorphism groups of curves in positive characteristic; Stöhr-Voloch theory; curves with many points over finite fields Hirschfeld, J. W.P.; Korchmáros, G.; Torres, F., Algebraic Curves over a Finite Field, Princeton Series in Applied Mathematics, (2008), Princeton University Press: Princeton University Press Princeton, NJ, MR 2386879 Curves over finite and local fields, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Finite ground fields in algebraic geometry, Positive characteristic ground fields in algebraic geometry, Algebraic coding theory; cryptography (number-theoretic aspects), Divisors, linear systems, invertible sheaves, Arithmetic ground fields for curves Algebraic 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 Nevanlinna's First Main Theorem; Nevanlinna's Second Main theorem; equidistribution theory of meromorphic mappings from the; Carlson- Griffiths viewpoint; defect relations; logarithmic derivative for meromorphic mappings; equidistribution theory of meromorphic mappings from the Carlson-Griffiths viewpoint Shiffman, B.: Introduction to the Carlson-Griffiths equidistribution theory. In: Lecture Notes in Math. \textbf{981}, 44-89 (1983) Value distribution theory in higher dimensions, Nevanlinna theory; growth estimates; other inequalities of several complex variables, Integration on analytic sets and spaces, currents, Integral geometry, Infinitesimal methods in algebraic geometry Introduction to the Carlson-Griffiths equidistribution 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 Tate-Shafarevich groups; abelian varieties over higher dimensional bases over finite fields; \(p\)-torsion in characteristic \(p > 0\); abelian varieties of dimension \(> 1\); étale and other Grothendieck topologies and cohomologies Abelian varieties of dimension \(> 1\), Étale and other Grothendieck topologies and (co)homologies, Arithmetic ground fields for abelian varieties On the \(p\)-torsion of the Tate-Shafarevich group of abelian varieties over higher dimensional bases 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 abc theorem for function fields,; Riemann Existence Theorem Umberto Zannier, Proof of the existence of certain triples of polynomials, Rend. Semin. Mat. Univ. Padova 117 (2007), 167 -- 174. Polynomials in general fields (irreducibility, etc.), Polynomials in real and complex fields: location of zeros (algebraic theorems), Riemann surfaces; Weierstrass points; gap sequences Proof of the existence of certain triples of polynomials | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic rational points of algebraic curves; theorem of Mordell-Weil; effectivity; Diophantine approximation [9] J. Cassels, \(Mordell's finite basis theorem revisited\). Math. Proc. of the Cambridge Phil. Soc. 100 (1986), 31-41. &MR 8 | &Zbl 0601. History of algebraic geometry, Rational points, History of mathematics in the 20th century, Cubic and quartic Diophantine equations, Higher degree equations; Fermat's equation, History of mathematics in the 19th century, Special algebraic curves and curves of low genus Mordell's finite basis theorem revisited | 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 characteristic; invariant theory; polynomials invariant under the group action; factorization of rings of invariants; Shephard-Todd theorem D.J. Benson, \textit{Polynomial Invariants of Finite Groups, London Mathematical Society Lecture Notes Series}, vol. 190 (Cambridge University Press, Cambridge, 1993) Actions of groups on commutative rings; invariant theory, Geometric invariant theory, Research exposition (monographs, survey articles) pertaining to commutative algebra, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry Polynomial invariants of finite 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 hyperbolic fibre space; higher dimensional analogue of Mordell's conjecture for curves; hyperbolic manifolds; algebraic families of hyperbolic varieties; Mordell's conjecture over function fields Noguchi, J.Hyperbolic fiber spaces and Mordell's conjecture over function fields, Publ. Research Institute Math. Sciences Kyoto University21, No. 1 (1985), 27--46. Hyperbolic and Kobayashi hyperbolic manifolds, Holomorphic bundles and generalizations, Families, moduli, classification: algebraic theory Hyperbolic fibre spaces and Mordell's conjecture 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 abelian Galois extensions; relative Brauer groups; cyclic extensions; indecomposable division algebras of prime exponent; central simple algebras; Brauer class; rational function fields Finite-dimensional division rings, Equations in general fields, Valued fields, Brauer groups of schemes, Separable extensions, Galois theory Dec groups for arbitrarily high exponents | 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; Brauer group; theorem of Davenport-Halberstam Serre, Jean-Pierre, Spécialisation des éléments de \(\operatorname{Br}_2(\mathbf{Q}(T_1, \ldots, T_n))\), C. R. Acad. Sci. Paris, Sér. I, 311, 7, 397-402, (1990) Brauer groups of schemes, Galois cohomology Spécialisation des éléments de \(Br_ 2({\mathbb{Q}}(T_ 1,\cdot \cdot \cdot,T_ n))\). (Specialization of elements of \(Br_ 2({\mathbb{Q}}(T_ 1,\cdot \cdot \cdot,T_ n)))\) | 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 Zariski dense orbits; Medvedev-Scanlon conjecture; Mordell-Lang theorem in positive characteristic for tori Arithmetic ground fields for abelian varieties, Rational points Zariski dense orbits for regular self-maps of tori 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 survey; diophantine approximation; elliptic curves; Falting's theorem; Catalan's equation; Baker's theorems; linear forms in logarithms Diophantine equations, Research exposition (monographs, survey articles) pertaining to number theory, Cubic and quartic Diophantine equations, Higher degree equations; Fermat's equation, Exponential Diophantine equations, Elliptic curves over global fields, Linear forms in logarithms; Baker's method, Abelian varieties and schemes Some fundamental methods in the theory of diophantine 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 prime characteristic; compute a set of generators for the ring of invariant functions Kempf, G. R.: More on computing invariants. Lecture notes in mathematics 1471, 87-89 (1991) Group actions on varieties or schemes (quotients), Geometric invariant theory, Computational aspects in algebraic geometry, Actions of groups on commutative rings; invariant theory More on computing invariants | 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; hypersurface; counting function; multiple exponential sum; singular locus; Deligne's bounds for exponential sums; number of points; hypersurfaces over finite fields Heath-Brown, DR, The density of rational points on nonsingular hypersurfaces, Proc. Indian Acad. Sci. Math. Sci., 104, 13-29, (1994) Arithmetic algebraic geometry (Diophantine geometry), Rational points, Estimates on exponential sums The density of rational points on non-singular hypersurfaces | 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; domain of regularity; Hilbert's irreducibility theorem Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Über die Kennzeichnung algebraischer Funktionenkörper durch ihren Regularitätsbereich | 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 equations over finite fields; elliptic curves; diophantine equations in two variables; quadratic residues; large sieve; Mordell's theorem; Riemann Roch theorem; rational points; integral points; Thue equation; superelliptic equations; nonstandard arithmetic; Hilbert's tenth problem Stepanov, SA: Arithmetic of Algebraic Curves Translated from the Russian by Irene Aleksanova. Monographs in Contemporary Mathematics. Consultants Bureau, New York (1994). Elliptic curves over global fields, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Elliptic curves, Elliptic curves over local fields, Multiplicative and norm form equations Arithmetic of algebraic curves. Transl. from Russian by Irene Aleksanova | 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 of affine variety; Hasse principle; ring of all algebraic integers; capacity theory on algebraic curves; completely valued algebraically closed fields; Hilbert's tenth problem; decision procedure for diophantine equations Rumelv, R. S., Arithmetic over the ring of all algebraic integers, Journal für die Reine und Angewandte Mathematik, 368, 127-133, (1986) Rational points, Decidability and field theory, Arithmetic ground fields for curves, Diophantine inequalities, Diophantine equations, Decidability of theories and sets of sentences Arithmetic over the ring of all algebraic integers | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic ring of invariants; action of finite group; prime characteristic; Steenrod algebra; modular invariants; Molien's theorem; Shepard-Todd theorem; polynomial rings; Cohen-Macaulay rings L. Smith, Polynomial Invariants of Finite Groups, A.\ K. Peters, Wellesley, 1995. Actions of groups on commutative rings; invariant theory, Geometric invariant theory, Research exposition (monographs, survey articles) pertaining to commutative algebra, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry Polynomial invariants of finite 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 two dimensional global fields; algebraic function field in one; variable over algebraic number field; Galois cohomology group; \(H^ 3\); Hasse principles; local-global principles; reduced norms; division algebras; quadratic forms; sum of squares K.~Kato, {A {H}asse principle for two dimensional global fields. With an appendix by {J}.-{L} {C}olliot-{T}hélène.}, J. Reine Angew. Math. {366} (1986), 142--180. DOI 10.1515/crll.1986.366.142; zbl 0576.12012; MR0833016 Galois cohomology, Brauer groups of schemes, Quadratic forms over global rings and fields, Galois cohomology, Quaternion and other division algebras: arithmetic, zeta functions, Waring's problem and variants, Arithmetic theory of algebraic function fields A Hasse principle for two dimensional global fields. Appendix by Jean-Louis Colliot-Thélène | 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 transcendental numbers; simultaneous diophantine approximations to coordinates of points; product of elliptic curves; measure for algebraic independence; Weierstrass elliptic function Robert Tubbs, A Diophantine problem on elliptic curves, Trans. Amer. Math. Soc. 309 (1988), no. 1, 325 -- 338. Algebraic independence; Gel'fond's method, Elliptic curves A diophantine problem 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 tensor products of cyclic algebras; division algebras of prime index; division algebras over function fields; cubic divisors; central division algebras; ramification divisors; Brauer groups; exponents Michel Van den Bergh, Division algebras on \?² of odd index, ramified along a smooth elliptic curve are cyclic, Algèbre non commutative, groupes quantiques et invariants (Reims, 1995) Sémin. Congr., vol. 2, Soc. Math. France, Paris, 1997, pp. 43 -- 53 (English, with English and French summaries). Finite-dimensional division rings, Arithmetic theory of algebraic function fields, Quaternion and other division algebras: arithmetic, zeta functions, Brauer groups of schemes Division algebras on \(\mathbb{P}^2\) of odd index, ramified along a smooth elliptic curve are cyclic | 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 valuation rings of function fields; coordinate ring of affine; variety over a real closed field; prime cone Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Valuations and their generalizations for commutative rings Constructions de places réelles dans géométrie semialgébrique. (Constructions of real places in semialgebraic geometry). (Thèse) | 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 lemniscatic sine function; lattice of periods; Riemann surface of genus \(1\); angle addition formulas for lemniscatic functions; constructible number; Abel's result Joel Langer and David Singer, The lemniscatic chessboard, Forum Geometricorum, Vol. 11 (2011), 183--199. Elliptic functions and integrals, Plane and space curves, Tilings in \(2\) dimensions (aspects of discrete geometry), Polyhedra and polytopes; regular figures, division of spaces The lemniscatic chessboard | 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 surface in projective space; function fields of surfaces; subfields of function fields of algebraic surfaces; dominant rational maps; plane curves Lee, Y; Pirola, G, On subfields of the function field of a general surface in \({\mathbb{P}}^3\), Int. Math. Res. Not., 24, 13245-13259, (2015) Surfaces of general type, Plane and space curves, Real and complex fields On subfields of the function field of a general surface in \(\mathbb{P}^{3}\) | 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 Riemann hypothesis in function-fields; algebro-geometric theory of curves and their correspondences Weil, André, Sur les courbes algébriques et les variétés qui s'en déduisent, Actual. Sci. Ind., vol. 1041, (1948), Hermann et Cie: Hermann et Cie Paris Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic problems in algebraic geometry; Diophantine geometry, Curves in algebraic geometry, Arithmetic algebraic geometry (Diophantine geometry), Divisors, linear systems, invertible sheaves, Riemann-Roch theorems Sur les courbes algébriques et les variétés qui s'en déduisent | 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 points of Drinfeld modules; arithmetic of function fields; class numbers; cyclotomic function fields; zeta-functions; Teichmüller characters; Artin conjecture; Artin L-series; p-adic measure; Main conjecture of Iwasawa theory; Frobenius; p-class groups; Bernoulli- Carlitz numbers Goss, D.: Analogies between global fields. Canad. math. Soc. conf. Proc. 7, 83-114 (1987) Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Fibonacci and Lucas numbers and polynomials and generalizations, Algebraic functions and function fields in algebraic geometry, Iwasawa theory, Cyclotomic extensions, Zeta functions and \(L\)-functions of number fields Analogies between global fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic singular primes in function fields; extension of field of constants; genus Stöhr, K-O, On singular primes in function fields, Arch. Math., 50, 156-163, (1988) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On singular primes 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 polarized \(K3\) surfaces; Tate's conjecture for \(K3\) surfaces; finitely generated fields of odd characteristic; Kuga-Satake abelian varieties Madapusi Pera, K., \textit{the Tate conjecture for K3 surfaces in odd characteristic}, Invent. Math., 201, 625-668, (2015) \(K3\) surfaces and Enriques surfaces The Tate conjecture for \(K3\) surfaces in odd characteristic | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic zeta functions; distribution of zeros; \(L\)-functions; finite fields; automorphic \(L\)-functions; GUE measure; Montgomery-Odlyzko law; normalized spacings; Wigner measure; Kolmogoroff-Smirnov discrepancy function; generalized Sato-Tate conjecture; low-lying zeros; \(L\)-functions of elliptic curves; spacings of eigenvalues; Haar measure; Fredholm determinants; Deligne's equidistribution theorem; monodromy; Kloosterman sums N.M. Katz and P. Sarnak. \textit{Random matrices, Frobenius eigenvalues, and monodromy, vol. 45 of American Mathematical Society Colloquium Publications}. American Mathematical Society, Providence, RI (1999). Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, \(\zeta (s)\) and \(L(s, \chi)\), Analytic computations, Structure of families (Picard-Lefschetz, monodromy, etc.), Varieties over finite and local fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, Limit theorems in probability theory Random matrices, Frobenius eigenvalues, and monodromy | 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 algebra of motivated cycles; standard conjectures; tannakian category; motivic Galois group; Hodge conjecture; Tate conjecture; algebraicity of the Lefschetz involution; base pieces; motivated \(E\)-correspondences; algebraic gerb; motivic cohomology; Hodge conjecture for abelian varieties; motif with integer coefficients; motives in characteristic \(p\); numerical equivalence coincides with homological equivalence André, Y., Pour une théorie inconditionnelle des motifs, Inst. Hautes études Sci. Publ. Math. No., 83, 5-49, (1996) (Co)homology theory in algebraic geometry, Generalizations (algebraic spaces, stacks), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Relations of \(K\)-theory with cohomology theories For an unconditional theory of motives | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic finite Galois coverings; finite graphs; \(L\)-functions; graph-theoretic version of the prime number theorem; Chebotarev's density theorem; density theorem for prime cycles K. Hashimoto, Artin type \(L\)-functions and the density theorem for prime cycles on finite graphs, Internat. J. Math. 3 (1992), no. 6, 809--826. Spectral theory; trace formulas (e.g., that of Selberg), Trees, Zeta functions and \(L\)-functions of number fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Artin type \(L\)-functions and the density theorem for prime cycles on finite graphs | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic function field of a smooth projective curve; characteristic \(p\); \(abc\) theorem [Sc] T. Scanlon: ''The abc theorem for commutative algebraic groups in characteristic p'', Int. Math. Res. Notices, No. 18, (1997), pp. 881--898. Arithmetic ground fields for abelian varieties, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry The \(abc\) theorem for commutative algebraic groups in characteristic \(p\) | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic geometric invariant theory; Diophantine approximation; Roth's theorem; Berkovich spaces; height of semi-stable points Geometric invariant theory, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation in probabilistic number theory, Rigid analytic geometry Diophantine applications of geometric invariant 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 specialization of local commutative formal groups; fields of prime characteristic M. Poletti : Iperalgebre su schiere valutanti (in corso di stampa su questi Anuali). Numdam | Zbl 0198.25802 Algebraic geometry Iperalgebre su schiere valutanti | 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; finite fields; hyperelliptic curves; lower bounds for moments; moments of \(L\)-functions; quadratic Dirichlet \(L\)-functions; random matrix theory Andrade, J. C.: Rudnick and soundararajan's theorem for function fields. Finite fields appl. 37, 311-327 (2016) Zeta and \(L\)-functions in characteristic \(p\), Curves over finite and local fields, Relations with random matrices, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Rudnick and Soundararajan's theorem for function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic geometric codes; algebraic curves over finite fields; function fields; Goppa codes; complexity of multiplication in extension fields; divisors of curves of genus 1; weight distributions; minimal weight Other types of codes, Geometric methods (including applications of algebraic geometry) applied to coding theory, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry Contributions to the theory of coding and complexity using algebraic function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic modular function \(j(\tau)\); singular moduli; prime factorization of the absolute norm; modular polynomial; arithmetic of maximal orders in quaternion algebras; geometry of supersingular elliptic curves; Fourier coefficients; Eisenstein series; Hilbert modular group; local heights; Heegner points Gross, B. H.; Zagier, D. B., \textit{on singular moduli}, J. Reine Angew. Math., 355, 191-220, (1985) Modular and automorphic functions, Algebraic moduli of abelian varieties, classification, Special algebraic curves and curves of low genus, Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Quaternion and other division algebras: arithmetic, zeta functions On singular moduli | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic real and complex curve singularities; branches of curve singularities; group of symmetries; permutation representation; modular characters for representations in characteristic 2; virtual modular characters; signed permutation representations; \(G\)-signature; \(G\)-equivariant \(C^ \infty\)-map germ; \(G\)-degree DOI: 10.1016/0040-9383(91)90040-B Differentiable maps on manifolds, Theory of singularities and catastrophe theory, Singularities of curves, local rings, Singularities in algebraic geometry, Complex singularities, Local complex singularities, Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants, Degree, winding number \(G\)-signature, \(G\)-degree, and symmetries of the branches of curve 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 equations; Bogomolov-Miyaoka inequality; arithmetic surfaces; small point conjecture; effective Mordell conjecture; Szpiro conjecture; branched coverings of curves; asymptotic Fermat theorem; abc-conjecture; height; effectivity Moret-Bailly, L., Hauteurs et classes de Chern sur LES surfaces arithmétiques, Astérisque, 183, 37-58, (1990) Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for curves, Arithmetic ground fields for surfaces or higher-dimensional varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields Heights and Chern classes on arithmetic 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 non-vanishing of \(L\)-functions; twisted \(L\)-functions of elliptic curves; function fields; elliptic curve rank in extensions Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Arithmetic ground fields for curves On the vanishing of twisted \(L\)-functions of elliptic curves over rational function fields | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic zeta and \(L\)-functions in characteristic \(p\); \(p\)-adic estimates for character sums; Newton polygons of curves Zeta and \(L\)-functions in characteristic \(p\), Exponential sums, Finite ground fields in algebraic geometry, Varieties over finite and local fields Hasse-Witt matrices for polynomials, 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 specialization of Galois extensions; function fields; Chebotarev property; Hilbert's irreducibility theorem; local and global fields Checcoli, S.; Dèbes, P.: Tchebotarev theorems for function fields. (2013) Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Hilbertian fields; Hilbert's irreducibility theorem, Field arithmetic, Arithmetic problems in algebraic geometry; Diophantine geometry Tchebotarev theorems 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 complexity of a Nash function; Nullstellensatz; Lojasiewicz inequality; approximation theorem of Efroymson R. Ramanakoraisina, Complexité des fonctions de Nash, Comm. Algebra 17 (1989), 1395-1406. Real algebraic and real-analytic geometry, Real-analytic and Nash manifolds Complexité des fonctions de Nash. (Complexity of Nash 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 higher dimensional analogues of Brauer-Siegel theorem; constant families of elliptic curves and abelian varieties; gap in proof of main theorem Varieties over finite and local fields, Finite ground fields in algebraic geometry, Elliptic surfaces, elliptic or Calabi-Yau fibrations Brauer-Siegel theorem for elliptic 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 Hilbert theorem 90 for K2; norm residue homomorphism; roots of unity; K- cohomology groups of Severi-Brauer varieties; \(K_ 2\) of division algebras; second Chow group; cohomology classes with zero restriction A. S. Merkur'ev and A. A. Suslin, ''The norm residue homomorphism,'' Preprint LOMI, P-6-82, Leningrad (1982). Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, \(K\)-theory of global fields, Étale and other Grothendieck topologies and (co)homologies, Grothendieck groups, \(K\)-theory, etc., (Equivariant) Chow groups and rings; motives Norm residue homomorphism | 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 theta divisor in the Jacobian of a non-hyperelliptic smooth curve; rank-4 double point; rank-4 quadrics conjecture; generic constructive Torelli theorem; infinitesimal deformation theory for the singularities of theta divisors SMITH (R.) , VARLEY (R.) . - Deformations of theta divisors and the rank 4 quadrics problem , Compositio Math., t. 76, 1990 , n^\circ 3, p. 367-398. Numdam | MR 92a:14025 | Zbl 0745.14012 Theta functions and curves; Schottky problem, Geometric invariant theory, Jacobians, Prym varieties, Theta functions and abelian varieties, Algebraic moduli of abelian varieties, classification, Singularities of curves, local rings, Local deformation theory, Artin approximation, etc., Singularities in algebraic geometry Deformations of theta divisors and the rank 4 quadrics problem | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic small fields of definition; real varieties; smooth approximation; generators for the \(K\)-theory of strongly algebraic vector bundles; algebraic model of compact differential manifold Ballico, E.: On the field of definition of vector bundles on real varieties,Geom. Dedicata 47 (1993), 317-325. Real algebraic sets, Relevant commutative algebra, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Topological \(K\)-theory On the field of definition of vector bundles on real 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 even terms of a multiple of the Chern character; Hodge bundles of semi-abelian schemes; torsion classes in Chow theory; explicit bounds for almost all prime powers appearing in their order; numerators of modified Bernoulli numbers Algebraic moduli of abelian varieties, classification, (Equivariant) Chow groups and rings; motives On the order of certain characteristic classes of the Hodge bundle of semi-abelian schemes | 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; p-adic number fields; diophantine equations; Bernoulli numbers; recurrent series; power series of algebraic; functions; Weierstrass preparation theorem; Newton polygon; Kronecker-Weber theorem; Jacobi sums; Hasse principle; Selmer; group; p-adic L-functions; rationality of power series J. W. S. Cassels, \textit{Local fields}, London Mathematical Society Student Texts, Vol. 3, Cambridge University Press, Cambridge, 1986. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Algebraic number theory: local fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Algebraic number theory: global fields, Elementary number theory, Diophantine equations Local 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 theory of algebraic curves; coding theory; Riemann-Roch theorem; function fields; differentials; Hasse-Weil theorem; geometric Goppa codes; trace codes H. Stichtenoth, Algebraic Function Fields and Codes, Second edn, (Springer-Verlag, Berlin Heidelberg, 2009). Zbl0816.14011 MR2464941 Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory, Research exposition (monographs, survey articles) pertaining to information and communication theory, Geometric methods (including applications of algebraic geometry) applied to coding theory, Cyclic codes Algebraic function fields and codes | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann-Roch theorem; tautological subring in the arithmetic Chow ring of bases of abelian schemes; Arakelov version of Hirzebruch proportionality principle; formula for a critical power of Hodge bundle. Arithmetic varieties and schemes; Arakelov theory; heights, Determinants and determinant bundles, analytic torsion, Riemann-Roch theorems A Hirzebruch proportionality principle in Arakelov geometry | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic finiteness of integral points; prime characteristic; abelian variety over a function field Voloch, J.F., Diophantine approximation on abelian varieties in characteristic \textit{p}, Amer. J. math., 117, 4, 1089-1095, (1995) Varieties over global fields, Algebraic theory of abelian varieties, Abelian varieties of dimension \(> 1\), Algebraic functions and function fields in algebraic geometry, Diophantine approximation, transcendental number theory Diophantine approximation on abelian varieties in characteristic \(p\) | 0 |
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic inter-universal Teichmüller theory; punctured elliptic curve; number field; mono-complex; étale theta function; 6-torsion points; height; explicit estimate; effective version; diophantine inequality; ABC conjecture; Szpiro conjecture; Fermat's last theorem Arithmetic ground fields for curves, Coverings of curves, fundamental group Explicit estimates in inter-universal Teichmüller 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 Diophantine approximation; arithmetic function field; Roth's theorem; Thue-Siegel method Approximation to algebraic numbers, Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Arithmetic varieties and schemes; Arakelov theory; heights Roth's theorem over arithmetic 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 functions; \(L\)-series; complex multiplication; \(p\)-adic uniformization; modular functions; Mordell-Weil theorem for function fields; canonical height; Néron-model; minimal model J.H. Silverman, in \(Advanced Topics in The Arithmetic of Elliptic Curves\), Graduate Texts in Mathematics, vol. 151 (Springer, New York, 1994) Elliptic curves, Arithmetic varieties and schemes; Arakelov theory; heights, Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic algebraic geometry (Diophantine geometry), Research exposition (monographs, survey articles) pertaining to algebraic geometry, Elliptic curves over local fields, Elliptic curves over global fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Advanced topics in the arithmetic of 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 Mordell's conjecture over function fields; theorem of the kernel . Coleman, R.F. , '' Manin's proof of the Mordell conjecture over function fields '', preprint. Rational points, Families, moduli of curves (algebraic), Algebraic functions and function fields in algebraic geometry Manin's proof of the Mordell conjecture 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 Castelnuovo-Mumford regularity; rational points in projective spaces over finite fields; Hilbert function; index of stability E. Kunz and R. Waldi, On the regularity of configurations of \(\mathbb{F}_q\)-rational points in projective space , J. Comm. Alg. 5 (2013), 269-280. Finite ground fields in algebraic geometry, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Rational points, Finite fields and commutative rings (number-theoretic aspects) On the regularity of configurations of \(\mathbb F_q\)-rational points in 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 finding of counter-examples; probabilistic approach to automated theorem proving in elementary geometry; polynomial identities; resultants; Sturm sequences; Wu-Ritt characteristic sets Mechanization of proofs and logical operations, Computational aspects in algebraic geometry Probabilistic verification of elementary geometry statements | 0 |
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