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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Kummer extension; rational function field; splitting of prime divisors; genus; smooth projective curve Xing, C. P.: Multiple Kummer Extensions and the Number of Prime Divisors of Degree One in Function Fields. J. of Pure and Appl. Algebra84, 85--93 (1993) Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic coding theory; cryptography (number-theoretic aspects), Algebraic functions and function fields in algebraic geometry Multiple Kummer extension and the number of prime divisors of degree one in function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Proceedings, conferences, collections, etc. pertaining to number theory, Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to information and communication theory, Curves over finite and local fields, Arithmetic theory of algebraic function fields, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Algebraic coding theory; cryptography (number-theoretic aspects), Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic), Automorphisms of curves, Cryptography, Shift register sequences and sequences over finite alphabets in information and communication theory, Semifields, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) Algebraic curves and finite fields. Cryptography and other applications. results of the workshops ``Applications of algebraic curves'' and ``Applications of finite fields'' of the RICAM Special Semester 2013
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic automorphisms of curves Schneps L.: Special Loci in Moduli Spaces of Curves. Mathematical Sciences Research Institute Publications, vol. 41, pp. 217--275. Cambridge University Press, London (2003) Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences, Automorphisms of curves, Coverings of curves, fundamental group, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Coverings in algebraic geometry Special loci in moduli spaces of curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic J.-H. Evertse and R. G. Ferretti, Diophantine inequalitites on projective varieties , Internat. Math. Res. Notices 2002 , no. 25, 1295--1330. \CMP1 903 776 Rational points, Diophantine inequalities, Diophantine inequalities Diophantine inequalities on projective varieties
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic chip firing game; sand pile Cori R., Le Borgne Y., On computation of Baker and Norine's rank on complete graphs, Electron. J. Combin. 23(1) (2016), Paper 1.31, 47 pp. Paths and cycles, Graphs and abstract algebra (groups, rings, fields, etc.), Riemann surfaces; Weierstrass points; gap sequences On computation of Baker and Norine's rank on complete graphs
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass gap sequence; Weierstrass semigroup; smooth plane curve; double covering of a curve; blowing-up of a rational surface Riemann surfaces; Weierstrass points; gap sequences, Plane and space curves, Coverings of curves, fundamental group, Rational and ruled surfaces Weierstrass gap sequences at points of curves on some rational surfaces
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic non-Euclidean crystallographic groups; bordered Riemann surfaces Bujalance, E., Gromadzki, G., Singerman, D.: On the number of real curves associated to a complex algebraic curve. Proc. Am. Math. Soc. 120(2), 507--513 (1994) Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences, Fuchsian groups and their generalizations (group-theoretic aspects) On the number of real curves associated to a complex algebraic curve
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic primitive roots; Artin's conjecture; function field; Dirichlet density of prime ideals Clark, D. A.; Kuwata, M.: Generalized Artin's conjecture for primitive roots and cyclicity mod p of elliptic curves over function fields. Canad. math. Bull. 38, No. 2, 167-173 (1995) Arithmetic theory of algebraic function fields, Elliptic curves over global fields, Elliptic curves Generalized Artin's conjecture for primitive roots and cyclicity mod \({\mathfrak p}\) of elliptic curves over function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Curves over finite and local fields, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Finite simple groups and their classification Applications of curves over finite fields. (Preface).
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic cyclic function fields; \(L\)-functions unctions of functions fields; mean value of \(L\)-functions; zeta functions; function; class number Rosen, M.: Average value of class numbers in cyclic extensions of the rational function field. In: Number Theory. (Halifax, NS, 1994), pp. 307-323, CMS Conference Proceedings, vol. 15. American Mathematical Society, Providence, RI (1995) Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Rate of growth of arithmetic functions, Other algebras and orders, and their zeta and \(L\)-functions, Class groups and Picard groups of orders, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry Average value of class numbers in cyclic extensions of the rational function field
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic tractability; function fields; genus one; quaternion algebra; global field Arithmetic theory of algebraic function fields, Brauer groups (algebraic aspects), Brauer groups of schemes Tractability of algebraic function fields in one variable of genus one over global fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic constellations; coverings; maps; dessins d'enfants; matrix integrals method; embedded graphs Lando, Sergei K.; Zvonkin, Alexander K., Graphs on surfaces and their applications, Encyclopaedia of Mathematical Sciences 141, \textrm{Low-Dimensional Topology, II}, xvi+455 pp., (2004), Springer-Verlag, Berlin Research exposition (monographs, survey articles) pertaining to combinatorics, Planar graphs; geometric and topological aspects of graph theory, Enumeration in graph theory, Riemann surfaces; Weierstrass points; gap sequences, Random matrices (algebraic aspects), Permutation groups, Braid groups; Artin groups, Riemann surfaces, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Relations of low-dimensional topology with graph theory, Low-dimensional topology of special (e.g., branched) coverings, Feynman diagrams, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Graphs on surfaces and their applications. Appendix by Don B. Zagier
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic complex algebraic curves; Teichmüller theory; elliptic curves; modular forms; Picard groups; hyperbolic geometry; classification of compact Riemann surfaces; moduli theory of compact Riemann surfaces Richard Hain, Moduli of Riemann surfaces, transcendental aspects, School on Algebraic Geometry (Trieste, 1999) ICTP Lect. Notes, vol. 1, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2000, pp. 293 -- 353. Families, moduli of curves (algebraic), Classification theory of Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Moduli of Riemann surfaces, transcendental aspects
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic meromorphic functions; Hurwitz spaces Natanzon, S.: Hurwitz spaces. London math. Soc. lecture note ser. 287, 165-177 (2001) Riemann surfaces; Weierstrass points; gap sequences, Compactness, Low-dimensional topology of special (e.g., branched) coverings, Compact Riemann surfaces and uniformization Hurwitz spaces
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic automorphic form; Drinfeld shtuka; Langlands correspondence; moduli stack of shtukas; global Langlands conjecture; function fields Laumon, G.: Chtoucas de Drinfeld et correspondance de Langlands. Gaz. Math. \textbf{88}, 11-33 (2001) Drinfel'd modules; higher-dimensional motives, etc., Langlands-Weil conjectures, nonabelian class field theory, Arithmetic theory of algebraic function fields, Algebraic moduli problems, moduli of vector bundles Drin'feld shtukas and Langlands correspondence (following Laurent Lafforgue)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Approximation in non-Archimedean valuations, Transcendence theory of elliptic and abelian functions, Complex multiplication and abelian varieties Algebraic values of \(p\)-adic elliptic functions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic graded Betti numbers; Green's conjecture; space curve; plane algebraic curve Loose, F, On the graded Betti numbers of plane algebraic curves, Manuscr. Math., 64, 503-514, (1989) Riemann surfaces; Weierstrass points; gap sequences, Plane and space curves On the graded Betti numbers of plane algebraic curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic division algebras; Brauer groups; rational function fields; ramification maps; central simple algebras A. S. Sivatski, L. H. Rowen and J.-P. Tignol, Division algebras over rational function fields in one variable, in Algebra and Number Theory, Proceedings of the Silver Jubilee Conference 2003, Hindustan Book Agency, New Delhi, 2005, pp. 158--180. Finite-dimensional division rings, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Division algebras over rational function fields in one variable.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Krichever-Novikov superalgebra; higher genus Riemann surface; BRST charge Virasoro and related algebras, Graded Lie (super)algebras, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Riemann surfaces; Weierstrass points; gap sequences, Supersymmetric field theories in quantum mechanics \(N=4\) Krichever-Novikov superalgebra on higher genus Riemann surfaces
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann surfaces; curves; Riemann-Roch theorem Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Riemann-Roch theorems, Chern characters Riemann-Roch theorem and Kodaira-Serre duality
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Algebraic curves; Algebraic functions of one variable Algebraic functions and function fields in algebraic geometry, Plane and space curves, Riemann surfaces; Weierstrass points; gap sequences Algebraic functions considered geometrically (continuation).
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic AG codes; algebraic geometric codes; function field tower; Gilbert-Varshamov bound; integral basis Arithmetic theory of algebraic function fields, Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Algebraic coding theory; cryptography (number-theoretic aspects) Integral bases in a tower of algebraic function fields: a contribution to the construction of asymptotically good algebraic-geometric codes
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass normal form; Tschirnhaus transformation Elliptic curves, Riemann surfaces; Weierstrass points; gap sequences, Computational aspects of algebraic curves, Symbolic computation and algebraic computation Tschirnhaus-Weierstrass curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic P. Vojta, On the \textit{ABC} conjecture and Diophantine approximation by rational points, Amer. J. Math. 122 (2000), no. 4, 843-872. Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Diophantine inequalities, Varieties over global fields, Heights, Diophantine inequalities, Global ground fields in algebraic geometry, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory On the \(abc\) conjecture and Diophantine approximation by rational points.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Tate's algorithm; Kodaira symbol; non-perfect residue field; resolution of singularities; vlow-up; elliptic scheme; Néron model; discrete valuation ring; Néron model of an elliptic curve; Weierstrass equation Bégueri, L.: Dualité sur un Corps Local à Corps Résiduel Algébriquement Clos. Mémoire de la Société Mathématique de France, vol. 4. Gauthier-Villars, Paris (1980) Minimal model program (Mori theory, extremal rays), Singularities of curves, local rings, Elliptic curves over global fields, Fibrations, degenerations in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Riemann surfaces; Weierstrass points; gap sequences, Other nonalgebraically closed ground fields in algebraic geometry Elliptic fibers over non-perfect residue fields.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic harmonic map; minimal surface; Riemann surface; Klein surface; Hopf differential Harmonic maps, etc., Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, Differential geometric aspects of harmonic maps, Riemann surfaces; Weierstrass points; gap sequences, Klein surfaces A factorization theorem for harmonic maps
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic automorphism group; period matrices; hyperelliptic Riemann surfaces Streit, M.: Period Matrices and Representation Theory. Abh. Math. Sem. Univ. Hamburg 71 (2001), 279-290. Automorphisms of curves, Period matrices, variation of Hodge structure; degenerations, Riemann surfaces; Weierstrass points; gap sequences, Riemann surfaces Period matrices and representation theory
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic functions; algebraic number fields Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Riemann surfaces The theory of algebraic functions of one variable.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass points; theta functions Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences Weierstrass points and the theta divisor
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic automorphism groups of algebraic function fields; realization of group as Galois group; Galois theory Henning Stichtenoth, Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer Funktionenkörper, Math. Z. 187 (1984), no. 2, 221 -- 225 (German). Separable extensions, Galois theory, Inverse Galois theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer Funktionenkörper
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic absolute Galois group of rational function field; real closed field; Tarski principle; transfer principle L P.D. v.d. Dries and P. Ribenboim , An application of Tarski's principle to absolute Galois groups of function fields , Queen's Mathematical Preprint No. 1984-8. Separable extensions, Galois theory, Ultraproducts and field theory, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Real algebraic and real-analytic geometry An application of Tarski's principle to absolute Galois groups of function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Creutz, B., Viray, B.: Two torsion in the Brauer group of a hyperelliptic curve. Manuscripta Math. (2014). 10.1007/s00229-014-0721-7 Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus, Brauer groups of schemes, Rational points Two torsion in the Brauer group of a hyperelliptic curve
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic derivatives of relative Wronskians; families of Weierstrass points; coarse moduli spaces of curves; Chow classes Gatto L., Trans. Amer. Math. Soc. 351 pp 2233-- (1999) Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic), Families, moduli of curves (analytic), Fine and coarse moduli spaces Derivatives of Wronskians with applications to families of special Weierstrass points
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Matrix models and tensor models for quantum field theory, Phase transitions (general) in equilibrium statistical mechanics, Critical phenomena in equilibrium statistical mechanics, Riemann surfaces; Weierstrass points; gap sequences Anomalous mechanisms of the loss of observability in non-Hermitian quantum models
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic curves; binary forms; genus 3; higher-order Weierstrass points; invariants Shaska, Tony; Shor, Caleb M., 2-Weierstrass points of genus 3 hyperelliptic curves with extra involutions, Comm. Algebra, 45, 5, 1879-1892, (2017) Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic), Automorphisms of curves 2-Weierstrass points of genus 3 hyperelliptic curves with extra involutions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic conjecture of Brumer-Stark; global function field; Bruhat-Tits tree; values of partial zeta functions Arithmetic theory of algebraic function fields, Local ground fields in algebraic geometry Rigid analytic methods in the arithmetic theory of function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic differential algebra; linear algebraic groups and torsors; patching; Picard-Vessiot theory; embedding problems; inverse differential Galois problem; Riemann surfaces Differential algebra, Linear algebraic groups over arbitrary fields, Riemann surfaces; Weierstrass points; gap sequences, Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain Differential embedding problems over complex function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic p-adic analytic functions; p-adic analytic subgroups of abelian varieties Analytic theory of abelian varieties; abelian integrals and differentials, Local ground fields in algebraic geometry, Arithmetic ground fields for abelian varieties, Approximation in non-Archimedean valuations, Non-Archimedean analysis, Transcendence (general theory) Sous-groupes à plusieurs paramètres \(p\)-adiques de variétés abéliennes
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic moduli space; plane branch; monomial curve; germs of irreducible plane curve singularities Singularities of curves, local rings, Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences, Formal methods and deformations in algebraic geometry The moduli of irreducible curve singularities with the semigroup \(\Gamma =<5,11>\)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic rational nodal curves; Weierstrass weight; number of nonsingular Weierstrass points Lax, R. F. and Widland, C.: Weierstraß points on rational nodal curves of genus 3,Canad. Math. Bull. 30 (1987), 286-294. Riemann surfaces; Weierstrass points; gap sequences, Singularities of curves, local rings Weierstrass points on rational nodal curves of genus 3
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann surfaces; Belyi functions; dessins d'enfants; Chebyshev polynomials G. Shabat, ''On a class of families of Belyi functions,'' in: \textit{Proc. of the} 12\textit{th International Conference FPSAC'00}, Springer-Verlag, Berlin (2000), pp. 575-581. Riemann surfaces; Weierstrass points; gap sequences, Other special orthogonal polynomials and functions, Compact Riemann surfaces and uniformization On a class of families of Belyi functions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic generalised elliptic functions; sigma functions; equivariance Riemann surfaces; Weierstrass points; gap sequences, Theta functions and abelian varieties, Jacobians, Prym varieties, Relationships between algebraic curves and integrable systems Generalised elliptic functions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Alonso, L. Martnez; Morino, E. Olmedilla: Algebraic geometry and soliton dynamics. Chaos, solitons \& fractals 5, No. 12, 2213-2227 (1995) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems, Riemann surfaces; Weierstrass points; gap sequences, Soliton equations Algebraic geometry and soliton dynamics.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass point; canonical model of a singular curve Singularities of curves, local rings, Riemann surfaces; Weierstrass points; gap sequences On the existence of smooth pseudoweierstrass points on a non-Gorenstein curve
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic subanalytic set; semianalytic set; rational point; height Pila, Jonathan, Rational points on a subanalytic surface, Université de Grenoble. Annales de l'Institut Fourier, 55, 1501-1516, (2005) Diophantine equations, Rational points, Real-analytic and semi-analytic sets, Semi-analytic sets, subanalytic sets, and generalizations, Heights Rational points on a subanalytic surface.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass point; numerical semigroup; stably rational; pointed curve; coarse moduli space 10.1090/S0002-9939-2014-11899-5 Riemann surfaces; Weierstrass points; gap sequences, Rational and unirational varieties, Special algebraic curves and curves of low genus, Rationality questions in algebraic geometry, Families, moduli of curves (algebraic) Irreducibility and stable rationality of the loci of curves of genus at most six with a marked Weierstrass point
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic curve; division algebra; algebraic index; period; Brauer group; period-index problem Skew fields, division rings, Arithmetic theory of algebraic function fields, Algebraic theory of abelian varieties The algebraic index of a division algebra
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic strong approximation; Brauer group; 1-motive David Harari, ``Le défaut d'approximation forte pour les groupes algébriques commutatifs'', Algebra Number Theory2 (2008) no. 5, p. 595-611 Group schemes, Galois cohomology, Approximation in non-Archimedean valuations, Adèle rings and groups The defect of strong approximation for commutative algebraic groups
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Function field; Jacobian; \(\ell\)-rank; L-polynomial Berger, Lisa; Hoelscher, Jing Long; Lee, Yoonjin; Paulhus, Jennifer; Scheidler, Renate: The \(\ell \)-rank structure of a global function field, Fields inst. Commun. 60, 145-166 (2011) Arithmetic theory of algebraic function fields, Class groups and Picard groups of orders, Algebraic number theory computations, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry The \(\ell\)-rank structure of a global function field
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Algebraic function; monodromy; Riemann surface; connectedness. Riemann surfaces; Weierstrass points; gap sequences On the monodromy group of an algebraic function belonging to a given Riemann surface
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic numerical semigroups; sparse semigroups; Weierstrass points; algebraic curves Contiero, A.; Moreira, C. G. T. A.; Veloso, P. M., On the structure of numerical sparse semigroups and applications to Weierstrass points, J. Pure Appl. Algebra, 219, 3946-3957, (2015) Commutative semigroups, Riemann surfaces; Weierstrass points; gap sequences, Computational aspects of algebraic curves On the structure of numerical sparse semigroups and applications to Weierstrass points.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic automorphisms; curves; numerical semigroups; Harbater-Katz-Gabber covers; zero \(p\)-rank; big actions; Galois module structure Automorphisms of curves, Riemann surfaces; Weierstrass points; gap sequences, Curves over finite and local fields, Commutative semigroups, Families, moduli of curves (algebraic) Automorphisms of curves and Weierstrass semigroups for Harbater-Katz-Gabber covers
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic global field of positive characteristic; Langlands conjecture; \(\ell\)-adic representations; Weil group; automorphic cuspidal representations; adele V. G. Drinfel\(^{\prime}\)d, Two-dimensional \?-adic representations of the Galois group of a global field of characteristic \? and automorphic forms on \?\?(2), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 134 (1984), 138 -- 156 (Russian, with English summary). Automorphic functions and number theory, II. Langlands-Weil conjectures, nonabelian class field theory, Representations of Lie and linear algebraic groups over global fields and adèle rings, Representation-theoretic methods; automorphic representations over local and global fields, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields Two-dimensional \(\ell\)-adic representations of the Galois group of a global field of characteristic \(p\) and automorphic forms on \(\mathrm{GL}(2)\)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic family of elliptic curves; Weierstraß form; lifted \(p\)-adic homology; zeta endomorphism \(p\)-adic cohomology, crystalline cohomology, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Riemann surfaces; Weierstrass points; gap sequences, Elliptic curves A \(p\)-adic cohomological method for the Weierstrass family and its zeta invariants
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic function fields; Klein surfaces; formally real fields Gamboa, JM, Compact Klein surfaces with boundary viewed as real compact smooth algebraic curves, Mem. Real Acad. Cienc. Exact. Fís. Nat. Madr., 27, iv+96, (1991) Arithmetic ground fields for curves, Klein surfaces, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to functions of a complex variable, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Arithmetic theory of algebraic function fields Compact Klein surfaces with boundary viewed as real compact smooth algebraic curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic doi:10.1016/S0550-3213(99)00510-6 String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Relationships between algebraic curves and physics, Riemann surfaces; Weierstrass points; gap sequences, Yang-Mills and other gauge theories in quantum field theory, Supersymmetric field theories in quantum mechanics Heterotic matrix string theory and Riemann surfaces
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic trigonal curves; Hurwitz spaces; Hassett-Keel program Deopurkar, A.: Compactifications of Hurwitz spaces, Int. math. Res. not. IMRN (2013) Families, moduli of curves (algebraic), Algebraic moduli problems, moduli of vector bundles, Stacks and moduli problems, Compactifications; symmetric and spherical varieties, Coverings of curves, fundamental group, Riemann surfaces; Weierstrass points; gap sequences Modular compactifications of the space of marked trigonal curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic n-th kind trigonal curve; total ramification points; gap sequences Coppens, M, The Weierstrass gap sequences of the total ramification points of trigonal coverings of \(\mathbb{P}^1\), Indag. Math., 47, 245-270, (1985) Coverings of curves, fundamental group, Riemann surfaces; Weierstrass points; gap sequences, Singularities of curves, local rings, Compact Riemann surfaces and uniformization The Weierstrass gap sequences of the total ramification points of trigonal coverings of \({\mathbb{P}}^ 1\)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Al functions; cyclic trigonal curves; sigma function Jacobians, Prym varieties, Elliptic curves, Special algebraic curves and curves of low genus, Riemann surfaces; Weierstrass points; gap sequences, Subvarieties of abelian varieties, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions The sigma function over a family of curves with a singular fiber
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann surface; period matrix; Torelli's theorem; Schottky's problem; Theta characteristics Silhol R., Complex Manifolds and Hyperbolic Geometry 311 pp 313-- (2001) Theta functions and curves; Schottky problem, Compact Riemann surfaces and uniformization, Period matrices, variation of Hodge structure; degenerations, Riemann surfaces; Weierstrass points; gap sequences Period matrices and the Schottky problem
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Galois covering of complete non-singular curves; Hasse-Witt invariants; differentials with poles; invariant effective divisors; Deuring- Shafarevich formula Nakajima, S., Equivariant form of the Deuring-šafarevič formula for Hasse-Witt invariants, Math. Z., 190, 559-566, (1985) Coverings of curves, fundamental group, Divisors, linear systems, invertible sheaves, Galois theory, Arithmetic theory of algebraic function fields Equivariant form of the Deuring-Šafarevič formula for Hasse-Witt invariants
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic covers; Riemann surfaces; monodromy; automorphisms Automorphisms of curves, Riemann surfaces; Weierstrass points; gap sequences On Galois group of factorized covers of curves
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic category; conformal structure; quasiconformal structure; Teichmüller map Riemann surfaces; Weierstrass points; gap sequences, Teichmüller theory for Riemann surfaces, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) Conformal and quasiconformal categorical representation of hyperbolic Riemann 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 Hasse-Weil bound; rational point; Weierstrass point; minimal curve; gap; genus; zeta function Viana, PH; Rodriguez, JEA, Eventually minimal curves, Bull. Braz. Math. Soc, 36, 39-58, (2005) Arithmetic ground fields for curves, Curves over finite and local fields, Rational points, Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus Eventually minimal curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic geometry; approximate algebra; computer algebra; algebraic function; root of the bivariate polynomial; analytic continuation; Riemann surface determination; Puiseux series K. Shiihara and T. Sasaki, Analytic continuation and Riemann surface determination of algebraic functions by computer. Japan J. Indust. Appl. Math.,13 (1996), 107--116. Numerical computation of solutions to single equations, Symbolic computation and algebraic computation, Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences Analytic continuation and Riemann surface determination of algebraic functions by computer
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Vojta's conjecture; hyperbolicity; heights; general type; rational points; moduli spaces Rational points, Heights, Families, moduli of curves (algebraic), Diophantine equations, Arithmetic ground fields for curves Bounding heights uniformly in families of hyperbolic varieties
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Girondo, E; González-Diez, G, Genus two extremal surfaces: extremal discs, isometries and Weierstrass points, Isr. J. Math., 132, 221-238, (2002) Compact Riemann surfaces and uniformization, General geometric structures on low-dimensional manifolds, Riemann surfaces; Weierstrass points; gap sequences Genus of two extremal surfaces: Extremal discs, isometries and Weierstrass points
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic hyperelliptic curve; asymptotic formula; finite field; Jacobian; torsion point; Betti numbers J. D. Achter, ''Results of Cohen-Lenstra type for quadratic function fields,'' in Computational Arithmetic Geometry, Providence, RI: Amer. Math. Soc., 2008, vol. 463, pp. 1-7. Curves over finite and local fields, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Arrangements of points, flats, hyperplanes (aspects of discrete geometry) Results of Cohen-Lenstra type for quadratic function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic rational interpolation; positive genus curve Riemann surfaces; Weierstrass points; gap sequences Rational interpolation on smooth curves with positive genus
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic function fields; homogeneous unit equation; derivations on function fields D. BROWNAWELL - D. MASSER, Vanishing sums in function fields, Math. Proc. Camb. Phil. Soc., 100 (1986), pp. 427-434. Zbl0612.10010 MR857720 Higher degree equations; Fermat's equation, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Vanishing sums in function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Klein surfaces; bordered Klein surfaces; automorphisms of Klein surfaces; NEC-groups Klein surfaces, Fuchsian groups and their generalizations (group-theoretic aspects), Riemann surfaces; Weierstrass points; gap sequences On symmetric representations of groups of automorphism of bordered Klein surfaces
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic special surfaces; modular varieties; Shimura varieties; Picard modular surfaces 10.4310/MRL.2008.v15.n6.a9 Modular and Shimura varieties, Arithmetic aspects of modular and Shimura varieties, Diophantine inequalities Irregular ball-quotient surfaces with non-positive Kodaira dimension
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic R. de Mello Koch, S. Ramgoolam, and C. Wen, On the refined counting of graphs on surfaces. Nuclear Phys. B 870 (2013), 530-581. Feynman diagrams, Applications of graph theory, Riemann surfaces; Weierstrass points; gap sequences, \(2\)-body potential quantum scattering theory, Electromagnetic interaction; quantum electrodynamics, Yang-Mills and other gauge theories in quantum field theory, Topological field theories in quantum mechanics On the refined counting of graphs on surfaces
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic commutative algebraic groups; linear forms; effective results; heights C. Fuchs and D. H. Pham, ''Commutative algebraic groups and \(p\)-adic linear forms,'' http://arxiv.org/pdf/1404.4209v1.pdf (2014). Linear forms in logarithms; Baker's method, Arithmetic algebraic geometry (Diophantine geometry), Approximation in non-Archimedean valuations, Group varieties Commutative algebraic groups and \(p\)-adic linear forms
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Division algebra; unit group; building; vector bundle; modification; Chern class; locally free sheaves of modules over Azumaya algebras: DOI: 10.1007/978-3-0346-0288-4_7 Varieties over finite and local fields, Quaternion and other division algebras: arithmetic, zeta functions, Arithmetic theory of algebraic function fields, Algebraic moduli problems, moduli of vector bundles Division algebras and unit groups on surfaces
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Fontanari C.: Moduli of curves via algebraic geometry. Liaison and related topics (Turin, 2001). Rend. Sem. Mat. Univ. Politec. Torino 59(2), 137--139 (2003) Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences Moduli of curves via algebraic geometry
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic complexity; fast polynomial multiplication; multiplicative complexity; linear coding; algebraic curves over finite fields Chudnovsky, D. V., Chudnovsky, G. V.: Algebraic complexities and algebraic curves over finite fields. Proc. Natl. Acad. Sci. USA84, 1739--1743 (1987) Analysis of algorithms and problem complexity, Software, source code, etc. for problems pertaining to field theory, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Algebraic complexities and algebraic curves over finite fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic intersection number Riemann surfaces; Weierstrass points; gap sequences, Plane and space curves Plane curves meeting at a point with high intersection multiplicity
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic function field analogue of the theory of elliptic modular curves; Drinfeld modules; Drinfeld's upper half-plane; expansions at the cusps of certain modular forms; Manin-Drinfeld theorem; algebraic modular forms; jacobian Ernst-Ulrich Gekeler, Drinfel\(^{\prime}\)d modular curves, Lecture Notes in Mathematics, vol. 1231, Springer-Verlag, Berlin, 1986. Modular and Shimura varieties, Arithmetic aspects of modular and Shimura varieties, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic ground fields for curves, Modular forms associated to Drinfel'd modules, Global ground fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Arithmetic theory of algebraic function fields Drinfeld modular curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Lang S: \textit{Elliptic Functions}. 2nd edition. Springer, New York; 1987. Curves in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic theory of algebraic function fields, Modular and automorphic functions, Algebraic functions and function fields in algebraic geometry, Complex multiplication and moduli of abelian varieties, Complex multiplication and abelian varieties, Research exposition (monographs, survey articles) pertaining to field theory Elliptic functions. Second edition
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic quadratic algebraic function fields; divisor class number two Le Brigand, D.: Classification of algebraic function fields with divisor class number two. Finite fields appl. 2, 153-172 (1996) Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry Classification of algebraic function fields with divisor class number two
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic AG code; Weierstrass gap; Hermitian curve Korchmáros, G.; Nagy, G.P., Lower bounds on the minimum distance in Hermitian one-point differential codes, Sci. China math., 56, 1449-1455, (2013) Applications to coding theory and cryptography of arithmetic geometry, Riemann surfaces; Weierstrass points; gap sequences, Algebraic coding theory; cryptography (number-theoretic aspects), Curves over finite and local fields, Geometric methods (including applications of algebraic geometry) applied to coding theory Lower bounds on the minimum distance in Hermitian one-point differential codes
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Zeta and \(L\)-functions in characteristic \(p\), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic theory of algebraic function fields \(L\)-functions of function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic arcs; ovals; convex curve; number of integer points; algebraic curves Enrico Bombieri & Jonathan Pila, ``The number of integral points on arcs and ovals'', Duke Math. J.59 (1989) no. 2, p. 337-357 Lattice points in specified regions, Diophantine equations, Lattices and convex bodies (number-theoretic aspects), Arithmetic algebraic geometry (Diophantine geometry), Rational points, Arithmetic problems in algebraic geometry; Diophantine geometry The number of integral points on arcs and ovals
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass gap sequence; singular points; Gorenstein curve Lax, R.F., Widland, C.: Gap sequences at a singularity, Pac. J. Math.150, 111--122 (1991) Singularities of curves, local rings, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Riemann surfaces; Weierstrass points; gap sequences Gap sequences at a singularity
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic automorphism groups of function fields; function fields over finite fields Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Automorphisms of curves, Applications to coding theory and cryptography of arithmetic geometry The asymptotic behavior of automorphism groups of function fields over finite fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstraß gap theorem; modular functions Riemann surfaces; Weierstrass points; gap sequences, Modular and automorphic functions, Partitions; congruences and congruential restrictions A proof of the Weierstraß gap theorem not using the Riemann-Roch formula
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Abelian integrals; Jacobi inversion problem Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization On algebraic differential expressions and on the Jacobi inversion problem. 3rd. Note.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Betti number of the moduli space of rank three stable Higgs bundles; Riemann surface; moment map; circle action Gothen, Peter B., The {B}etti numbers of the moduli space of stable rank~{\(3\)} {H}iggs bundles on a {R}iemann surface, International Journal of Mathematics, 5, 6, 861-875, (1994) Vector bundles on curves and their moduli, Riemann surfaces; Weierstrass points; gap sequences, Algebraic moduli problems, moduli of vector bundles, Complex-analytic moduli problems, Families, moduli of curves (analytic), Étale and other Grothendieck topologies and (co)homologies, Riemann surfaces The Betti numbers of the moduli space of stable rank 3 Higgs bundles on a Riemann surface
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic function field; quadratic field; ideal class group Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry, Quadratic extensions On imaginary quadratic function fields with ideal class group of exponent \(\leq 2\)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic function fields; Weil differentials; Weierstrass points; Riemann hypothesis; zeta functions; coding theory Goldschmidt, D. M.: Algebraic functions and projective curves, Grad texts in math. 215 (2003) Algebraic functions and function fields in algebraic geometry, Zeta functions and \(L\)-functions of number fields, Arithmetic theory of algebraic function fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Applications to coding theory and cryptography of arithmetic geometry Algebraic functions and projective curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Brill-Noether theory; Weierstrass \(n\)-ples Riemann surfaces; Weierstrass points; gap sequences, Special divisors on curves (gonality, Brill-Noether theory) Pointed curves and Weierstrass points
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Galois tower; modular tower; Galois closure; function field Bassa, A.; Beelen, P.: On the construction of Galois towers, Contemp. math. 487, 9-20 (2009) Algebraic functions and function fields in algebraic geometry, Galois theory, Arithmetic theory of algebraic function fields, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) On the construction of Galois towers
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic regular minimal model of curve; Arakelov intersection; boundedness of the average height of Weierstrass points Jean-François Burnol, Weierstrass points on arithmetic surfaces, Invent. Math. 107 (1992), no. 2, 421 -- 432. Arithmetic varieties and schemes; Arakelov theory; heights, Riemann surfaces; Weierstrass points; gap sequences Weierstrass points on arithmetic surfaces
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic moduli space; vector bundle over Riemann surface; Chern class Arnaud Beauville, Sur la cohomologie de certains espaces de modules de fibrés vectoriels, Geometry and analysis (Bombay, 1992) Tata Inst. Fund. Res., Bombay, 1995, pp. 37 -- 40 (French). Classical real and complex (co)homology in algebraic geometry, Algebraic moduli problems, moduli of vector bundles, Characteristic classes and numbers in differential topology, Riemann surfaces; Weierstrass points; gap sequences, Vector bundles on curves and their moduli On the cohomology of certain moduli spaces of vector bundles
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic equations; solvability problems; Abel's theorem; complex functions of one variable; Riemann surfaces; monodromy; differential Galois theory; regular polyhedra Separable extensions, Galois theory, Classification theory of Riemann surfaces, Research exposition (monographs, survey articles) pertaining to field theory, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory, Equations in general fields, Riemann surfaces; Weierstrass points; gap sequences, Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain, Differential algebra Abel's theorem in problems and solutions. Based on the lectures of Professor V. I. Arnold. With a preface and an appendix by Arnold and an appendix by A. Khovanskii.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic duality in cohomology; curve; abelian variety; derived category; Serre duality; pairing Étale and other Grothendieck topologies and (co)homologies, Abelian varieties of dimension \(> 1\), Group schemes, Arithmetic theory of algebraic function fields, Algebraic theory of abelian varieties Duality for cohomology of curves with coefficients in abelian varieties
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic IST method; deformation of algebraic curves; Yang-Mills equations; KdV equation; finite-gap solution; evolution equations; Heisenberg magnet; KP equation KdV equations (Korteweg-de Vries equations), Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic) Deformations of algebraic curves and integrable nonlinear evolution equations
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann surfaces; genus; isotopy; Teichmüller spaces; moduli spaces of curves Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Surfaces which in fact are curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic real algebraic curve; theta characteristics; number of real bitangents Topology of real algebraic varieties, Theta functions and abelian varieties, Riemann surfaces; Weierstrass points; gap sequences On theta characteristics of real algebraic curves
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