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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 Garcia-Stichtenoth tower; zeta function; Jacobian variety Mcguire, Gary; Zaytsev, Alexey: On the zeta functions of an optimal tower of function fields over F4, Contemp. math. 518, 327-338 (2010) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves On the zeta functions of an optimal tower of function fields over \(\mathbb{F}_4\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Jacquet modules; representations; split \(p\)-adic reductive groups; prehomogeneous vector spaces; Whittaker functions; Chern classes of vector bundles; unramified principal series representations; Kazhdan- Lusztig modules; Whittaker model; flag manifolds; affine Weyl groups; Iwahori-spherical representations Mark Reeder, Whittaker functions, prehomogeneous vector spaces and standard representations of \?-adic groups, J. Reine Angew. Math. 450 (1994), 83 -- 121. Representations of Lie and linear algebraic groups over local fields, Analysis on \(p\)-adic Lie groups, Harmonic analysis on homogeneous spaces, Homogeneous spaces and generalizations Whittaker functions, prehomogeneous vector spaces and standard representations of \(p\)-adic groups
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Zariski theorem on fundamental group; complement of a normal crossing divisor Lê D\tilde{}ung Tráng and Kyoji Saito. The local \({\pi}\)1of the complement of a hypersurface with normal crossings in codimension 1 is abelian. Ark. Mat., 22(1):1--24, 1984. Homotopy theory and fundamental groups in algebraic geometry, Low codimension problems in algebraic geometry, Coverings in algebraic geometry The local \(\pi _ 1\) of the complement of a hypersurface with normal crossings in codimension 1 is abelian
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic height function; elliptic curves over function fields; specialization map Elliptic curves over global fields, Heights, Arithmetic varieties and schemes; Arakelov theory; heights Heights and the specialization map for families of elliptic curves over \(\mathbb {P}^n\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Christol, G.; Mebkhout, Z., Sur le théorème de l\(###\)indice des équations différentielles \textit{p}-adiques IV, Invent. Math., 143, 629-672, (2001) \(p\)-adic differential equations, \(p\)-adic cohomology, crystalline cohomology, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc., Local ground fields in algebraic geometry On the index theorem for \(p\)-adic differential equations. IV
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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 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Étale and other Grothendieck topologies and (co)homologies, Arithmetic ground fields for abelian varieties, Arithmetic varieties and schemes; Arakelov theory; heights An open adelic image theorem for motivic representations over function fields
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(p\)-adic Galois representation; filtered \((\phi; N)\)-modules L. Berger, Équations différentielles p-adiques et {({\(\phi\)},N)}-modules filtrés, Représentations p-adiques de groupes p-adiques I. Représentations galoisiennes et {({\(\phi\)},{\(\Gamma\)})}-modules, Astérisque 319, Société Mathématique de France, Paris (2008), 13-38. Galois representations, \(p\)-adic theory, local fields, \(p\)-adic differential equations, \(p\)-adic cohomology, crystalline cohomology \(p\)-adic differential equations and filtered \((\varphi, N)\)-modules
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic divisor class group of affine surface P. Blass and J. Lang , A method for computing the kernel of a map of divisor classes of local rings in characteristic p \neq 0 , Mich. Math. J. 35 (1988). Regular local rings, Divisors, linear systems, invertible sheaves, Special surfaces A method for computing the kernel of a map of divisor classes of local rings in characteristic p\(\neq 0\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Huneke issue; maximal Cohen-Macaulay modules; syzygies; hypersurface rings; stable module category Syzygies, resolutions, complexes and commutative rings, Cohen-Macaulay modules, Singularities of surfaces or higher-dimensional varieties Some extensions of theorems of Knörrer and Herzog-Popescu
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass 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. Semenov and M. Zhykhovich, Integral motives, relative Krull-Schmidt principle, and Maranda-type theorems, Math. Ann., 363 (2015), no. 1-2, 61--75. Zbl 06488199 MR 3394373 (Equivariant) Chow groups and rings; motives Integral motives, relative Krull-Schmidt principle, and Maranda-type theorems
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Abelian differential; branched coverings Differentials on Riemann surfaces, Coverings of curves, fundamental group On a theorem of O. Haupt characterizing periods of Abelian differentials
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(K3\) surface; surface with \(p_g=q=2\); isomorphism of Hodge structures; product-quotient surface Surfaces of general type, (Equivariant) Chow groups and rings; motives, Families, moduli, classification: algebraic theory, Transcendental methods, Hodge theory (algebro-geometric aspects) On the cohomology of surfaces with \(p_g = q = 2\) and maximal Albanese dimension
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic twin irreducible polynomials; parity barrier over function fields; short character sums; level of distribution for irreducible polynomials Étale and other Grothendieck topologies and (co)homologies, Arithmetic theory of algebraic function fields, Polynomials over finite fields, Goldbach-type theorems; other additive questions involving primes, Primes in congruence classes On the Chowla and twin primes conjectures over \(\mathbb{F}_q[T]\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic modular function fields; principal congruence subgroups of prime level; algorithm; Newton polygon N. Ishida, N. Ishii, The equations for modular function fields of principal congruence subgroups of prime level. Manuscripta Math. 90 (1996), no. 3, 271-285. Zbl0871.11031 MR1397657 Modular and automorphic functions, Algebraic functions and function fields in algebraic geometry The equations for modular function fields of principal congruence subgroups of prime level
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Schmidt's subspace theorem; function fields; Thue's equation Other nonalgebraically closed ground fields in algebraic geometry, Thue-Mahler equations An effective Schmidt's subspace theorem for non-linear forms over function fields
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic differential forms; cdh-topology; valuation rings; seminormalization; singularities Positive characteristic ground fields in algebraic geometry, Étale and other Grothendieck topologies and (co)homologies Differential forms in positive characteristic. II: cdh-descent via functorial Riemann-Zariski spaces
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Bloch-Ogus complex; Brauer group; cohomological Hasse principle; Henselian pair; absolute purity theorem; regular local ring; spectral sequence; positive characteristic Matsumi K.: A Hasse principle for three-dimensional complete local rings of positive characteristic. J. Reine Angew. Math. 542, 113--121 (2002) Regular local rings, (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.), Schemes and morphisms A Hasse principle for three-dimensional complete local rings of positive characteristic
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Rational points Rational points in their fiber: complements to a theorem of Poonen
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass 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. Kollár and K. Nowak, Continuous rational functions on real and \textit{p}-adic varieties, Math. Z. 279 (2015), 85-97. Semialgebraic sets and related spaces, Real rational functions Continuous rational functions on real and \(p\)-adic varieties
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Abbes, A; Saito, T, Analyse micro-locale \(l\)-adique en caractéristique \(p>0\): le cas d'un trait, Publ. Res. Inst. Math. Sci., 45, 25-74, (2009) Ramification and extension theory, Étale and other Grothendieck topologies and (co)homologies Microlocal \(\ell \)-adic analysis in characteristic \(p>0\) in the case of a trait
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic elliptic surface; finite field; Brauer--Siegel theorem Zykin, A.: On the Brauer-Siegel theorem for families of elliptic surfaces over finite fields, Mat. zametki 86, No. 1, 148-150 (2009) Elliptic surfaces, elliptic or Calabi-Yau fibrations, Elliptic curves over global fields, Zeta and \(L\)-functions: analytic theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry Brauer-Siegel theorem for families of elliptic surfaces over finite fields
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Heegner point; Shimura curve; Cherednik-Drinfeld prime; Atkin-Lehner involution Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties Automorphisms and reduction of Heegner points on Shimura curves at Čerednik-Drinfeld primes
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic tame action of finite group; \(L\)-functions; de Rham homology; \(\varepsilon\)-constants; Galois extension; Euler class T. Chinburg, B. Erez, G. Pappas, and M. J. Taylor, ''\(\epsilon\)-constants and the Galois structure of de Rham cohomology,'' Ann. of Math., vol. 146, iss. 2, pp. 411-473, 1997. de Rham cohomology and algebraic geometry, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Drinfel'd modules; higher-dimensional motives, etc. \(\varepsilon\)-constants and the Galois structure of de Rham cohomology
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic local-global principle; abelian varieties P. Jossen, A. Perucca, A counterexample to the local-global principle of linear dependence for abelian varieties, C. R. Acad. Sci. Paris, Ser. I 348 (2010), no. 1, 9--10. Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian varieties A counterexample to the local-global principle of linear dependence for abelian varieties
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic basepoint-freeness; b-divisors; saturation Fujino, O.: Base point free theorems--saturation, B-divisors and canonical bundle formula. Algebra Number Theory, to appear. arXiv:math/0508554v3 Divisors, linear systems, invertible sheaves, Adjunction problems, Minimal model program (Mori theory, extremal rays) Basepoint-free theorems: saturation, b-divisors, and canonical bundle formula
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic affine variety minus bound on the height of integral points; hyperplanes in general position; number of integral points; function fields Wang, J.T.-Y., \textit{S}-integral points of \(\mathbb{P}^n - \{2 n + 1 \text{ hyperplanes in general position} \}\) over number fields and function fields, Trans. amer. math. soc., 348, 3379-3389, (1996) Arithmetic theory of algebraic function fields, Rational points, Varieties over global fields \(S\)-integral points of \(\mathbb{P}^ n- \{2n+1\) hyperplanes in general position\(\}\) over number fields and function fields
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic prehomogeneous vector space; reductive group Gyoja, A.: A theorem of Chevalley type for prehomogeneous vector spaces. J. math. Soc. Japan 48, 161-167 (1996) Simple, semisimple, reductive (super)algebras, Grassmannians, Schubert varieties, flag manifolds, Representation theory for linear algebraic groups A theorem of Chevalley type for prehomogeneous vector spaces
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic finite ground fields; zeta functions; foliations; dynamical systems; differential operators; index theory Arithmetic ground fields for abelian varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Abelian varieties of dimension \(> 1\), Foliations in differential topology; geometric theory, Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) On abelian varieties and the transversal index theorem
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(K3\) surfaces; arithmetic geometry; algebraic geometry; \(p\)-adic methods; good reduction criterion; monodromy criterion; Kulikov degeneration \(K3\) surfaces and Enriques surfaces, Local ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Finite ground fields in algebraic geometry, Varieties over finite and local fields A Kulikov-type classification theorem for a one parameter family of \(K3\)-surfaces over a \(p\)-adic field and a good reduction criterion
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass 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 function; Grassmannian A. Eremenko and A. Gabrielov, ''Elementary proof of the B. and M. Shapiro conjecture for rational functions,'' , preprint , 2005. Grassmannians, Schubert varieties, flag manifolds, Enumerative problems (combinatorial problems) in algebraic geometry, Real algebraic and real-analytic geometry, Real rational functions An elementary proof of the B. and M. Shapiro conjecture for rational functions
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Vector bundles on curves and their moduli A note on dormant opers of rank \(p-1\) in characteristic \(p\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic geometry Global ground fields in algebraic geometry The Mordell conjecture for function fields [after H. Grauert]
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic APN functions; finite fields; absolute irreducible polynomials Férard, E, On the irreducibility of the hyperplane sections of Fermat varieties in \(\mathbb {P}^{3}\)\(\mathbb{P}\)3 in characteristic 2, Adv. Math. Commun., 8, 497-509, (2014) Polynomials over finite fields, Polynomials in general fields (irreducibility, etc.), Computational aspects of algebraic surfaces, Algebraic coding theory; cryptography (number-theoretic aspects) On the irreducibility of the hyperplane sections of Fermat varieties in \(\mathbb{P}^3\) in characteristic \(2\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic log-canonical pairs; Du Bois; Kawamata-Viehweg-Nadel vanishing O. Fujino, A remark on Kovács's vanishing theorem , Kyoto J. Math. 52 (2012), 829-832. Vanishing theorems in algebraic geometry, Minimal model program (Mori theory, extremal rays) A remark on Kovács's vanishing theorem
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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 L. Lafforgue, La correspondance de Langlands sur les corps de fonctions, preprint. Representation-theoretic methods; automorphic representations over local and global fields, Formal groups, \(p\)-divisible groups On the Ramanujan-Petersson conjecture over function fields. I: Geometric study
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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 rigid analytic spaces; determinants; Galois representations; eigenvarieties 23. Chenevier, Gaëtan The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings in Automorphic forms and Galois representations. Vol. 1London Math. Soc. Lecture Note Ser.414 (2014) 221--285 Math Reviews MR3444227 Galois representations, Representations of Lie and linear algebraic groups over local fields, Rigid analytic geometry, General commutative ring theory, \(p\)-adic theory, local fields The \(p\)-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings
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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 universally open morphism; valued field Moret-Bailly, L.: Un théorème d'application ouverte sur LES corps valués algébriquement clos, Math. scand. 111, 161-168 (2012) Elementary questions in algebraic geometry, Local ground fields in algebraic geometry A theorem on an open mapping over algebraically closed fields with valuation
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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 integral closure; local cohomology; big Cohen-Macaulay modules; characteristic p Quy, PH, On the vanishing of local cohomology of the absolute integral closure in positive characteristic, J. Algebra, 456, 182-189, (2016) Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Local cohomology and commutative rings, Étale and flat extensions; Henselization; Artin approximation, Homological conjectures (intersection theorems) in commutative ring theory, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Local cohomology and algebraic geometry On the vanishing of local cohomology of the absolute integral closure in positive characteristic
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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 Brauer group; Tate-Shafarevich group; Tate's conjecture \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Positive characteristic ground fields in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties, Varieties over finite and local fields, Varieties over global fields Tate's conjecture and the Tate-Shafarevich group over global 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 Weierstrass family of elliptic curves; lifted p-adic homology G. C. Kato, Lifted \( p\)-adic homology with compact supports of Weierstrass family and zeta matrices (in preparation). Elliptic curves, Families, moduli of curves (algebraic), \(p\)-adic cohomology, crystalline cohomology Lifted p-adic homology with compact supports of the Weierstrass family and its zeta endomorphism
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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 Calabi-Yau variety; Artin-Mazur height; liftability to characteristic zero; Witt vectors de Rham cohomology and algebraic geometry Quasi-Frobenius splitting and lifting of Calabi-Yau varieties in characteristic \(p\)
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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 varieties of dimension \(> 1\), Jacobians, Prym varieties Corrigendum to: ``The rational points on certain abelian varieties 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 Radon transform; second main theorem for holomorphic curves; Abelian varieties --, Holomorphic curves in abelian varieties: the second main theorem and applications.Japan. J. Math. (N.S.), 26 (2000), 129--152. Value distribution theory in higher dimensions, Analytic theory of abelian varieties; abelian integrals and differentials Holomorphic curves in abelian varieties: the second main theorem and applications
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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; prime divisor; Galois theory Pop, F, Pro-\(\mathcall \) abelian-by-central Galois theory of prime divisors, Isr. J. Math., 180, 43.68, (2010) Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry Pro-\(\ell\) abelian-by-central Galois theory of prime divisors
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic decidability; function field; analogue of Hilbert's tenth problem A. Shlapentokh, ''Diophantine undecidability of function fields of characteristic greater than 2 finitely generated over a field algebraic over a finite field,'' Comp. Math., 132, No.1, 99--120 (2002). Model-theoretic algebra, Decidability (number-theoretic aspects), Undecidability and degrees of sets of sentences, Decidability of theories and sets of sentences, Decidability and field theory, Global ground fields in algebraic geometry Diophantine undecidability of function fields of characteristic greater than 2, finitely generated over fields algebraic over a finite 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 genus zero Gopakumar-Vafa invariants; Calabi-Yau manifolds V. Vologodsky, \textit{Integrality of instanton numbers}, arXiv:0707.4617. Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Mirror symmetry (algebro-geometric aspects), Calabi-Yau manifolds (algebro-geometric aspects), Miscellaneous applications of number theory, Topological field theories in quantum mechanics, Étale and other Grothendieck topologies and (co)homologies Integrality of instanton numbers and \(p\)-adic B-model
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Laplace hyperfunctions; vanishing theorem; sheaf of Laplace hyperfunctions Hyperfunctions, analytic functionals, Hyperfunctions, Homology and cohomology theories in algebraic topology A cohomology vanishing theorem and Laplace hyperfunctions with holomorphic parameters
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Dutta multiplicity; Chern characters; Adams operation; complexes; Euler characteristic; Frobenius map Kurano, Kazuhiko; Roberts, Paul C., Adams operations, localized {C}hern characters, and the positivity of {D}utta multiplicity in characteristic {\(0\)}, Transactions of the American Mathematical Society, 352, 3103-3116, (2000) Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Grothendieck groups, \(K\)-theory and commutative rings, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Applications of methods of algebraic \(K\)-theory in algebraic geometry Adams operations, localized Chern characters, and the positivity of Dutta multiplicity in characteristic \(0\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic abelian varieties; function fields; arithmetic duality, Galois cohomology Izquierdo, D., Variétés abéliennes sur les corps de fonctions de courbes sur des corps locaux, Doc. Math., 22, 297-361, (2017) Arithmetic ground fields for abelian varieties, Geometric class field theory, Rational points, Algebraic functions and function fields in algebraic geometry, Galois cohomology, Étale and other Grothendieck topologies and (co)homologies, Local ground fields in algebraic geometry Abelian varieties for function fields of curves over local fields
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Chern class; Segre class; enveloping algebra; semisimple Lie algebra; cohomology class; flag variety; Goldie rank polynomial; nilpotent varieties; primitive ideals Borho, W., Brylinski, J.-L., MacPherson, R.: A note on primitive ideals and characteristic classes. In. Geometry today. Arbarello, E., Procesi, C., Strickland, E.(eds.), pp. 11-20. Boston, Basel, Stuttgart: Birkhäuser 1985 Universal enveloping (super)algebras, Group actions on varieties or schemes (quotients) A note on primitive ideals and characteristic classes
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Jacobian conjecture; Wright's conjecture Jacobian problem, Polynomial rings and ideals; rings of integer-valued polynomials, Trees A counterexample to a conjecture of Wright on homogeneous polynomial maps associated with rooted trees
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass 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 cohomology; specialization map; slope filtration; trace morphism Étale and other Grothendieck topologies and (co)homologies, \(p\)-adic cohomology, crystalline cohomology On the \(p\)-adic local invariant cycle theorem
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Artin-Schreier-Witt theory; torsors; degeneration; group schemes Mohamed Saïdi, On the degeneration of étale \?/\?\? and \?/\?²\?-torsors in equal characteristic \?>0, Hiroshima Math. J. 37 (2007), no. 2, 315 -- 341. Coverings of curves, fundamental group, Coverings in algebraic geometry, Fibrations, degenerations in algebraic geometry, Formal methods and deformations in algebraic geometry On the degeneration of étale \(\mathbb Z/p\mathbb Z\) and \(\mathbb Z/p^2\mathbb Z\)-torsors in equal characteristic \(p>0\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic projective variety; finite field; action by a finite group; complex representation; functional equation for \(L\)-function; Euler characteristic Chinburg T. , Erez B. , Pappas G. , Taylor M.J. , On the \epsilon -constants of a variety over a finite field , Amer. J. Math. 119 ( 1997 ) 503 - 522 . Zbl 0927.14013 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Group actions on varieties or schemes (quotients), Homogeneous spaces and generalizations, Varieties over finite and local fields On the \(\varepsilon\)-constants of a variety over a finite field
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(p\)-adic uniformization of Shimura curves; nonarchimedean upper half plane; theorem of Cherednik and Drinfeld; rigid-analytic variety; Mumford curves Boutot, J.-F.; Carayol, H., Uniformisation \textit{p}-adique des courbes de Shimura: les théorèmes de Čerednik et de Drinfeld, Astérisque, 196-197, 45-158, (1991) Local ground fields in algebraic geometry, Modular and Shimura varieties, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic ground fields for curves, Formal groups, \(p\)-divisible groups \(p\)-adic uniformization of Shimura curves: the theorems of Cherednik and Drinfeld
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic local Pfister conjecture; fields of rational functions Finite-dimensional division rings, Quadratic forms over general fields, Forms over real fields, Brauer groups (algebraic aspects), Skew fields, division rings, Algebraic functions and function fields in algebraic geometry, Rational and ruled surfaces \(\Omega\)-algebras over fields of rational functions with special fields of constants.
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Divisors, linear systems, invertible sheaves, Transcendental methods, Hodge theory (algebro-geometric aspects), Sheaves in algebraic geometry Cayley-Bacharach theorems with excess vanishing
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass 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 cohomology, crystalline cohomology, \(p\)-adic differential equations The \(p\)-adic local monodromy theorem for fake annuli
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic finite ground field; zeta-function S. Lichtenbaum. Zeta functions of varieties over finite fields at s = 1. In Arithmetic and Geometry, Vol. I, volume 35 of Progr. Math., pages 173--194. Birkh''auser Boston, Boston, MA, 1983. Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry Zeta-functions of varieties over finite fields at \(s=1\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Actions of groups on commutative rings; invariant theory, Group actions on varieties or schemes (quotients) An integrality theorem of Grosshans over arbitrary base ring
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Euler-Poincaré polynomial; canonical line bundle; Chern classes; Todd class; Bernoulli polynomials; Hirzebruch Riemann-Roch formula Riemann-Roch theorems, Characteristic classes and numbers in differential topology, Topological properties in algebraic geometry The Riemann-Roch theorem and Bernoulli polynomials
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic abelian variety; characteristic polynomials S. Haloui and V. Singh, The characteristic polynomials of abelian varieties of dimension \(4\) over finite fields , in Arithmetic, Geometry, Cryptography and Coding Theory: 13th Conference [on] Arithmetic, Geometry, Cryptography and Coding Theory, CIRM, Marseille, France, March 14-18, 2011: Geocrypt 2011, Bastia, France, June 19-24, 2011 , volume 574, page 59. American Mathematical Soc., 2012. Finite ground fields in algebraic geometry, Polynomials in number theory, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian varieties The characteristic polynomials of abelian varieties of dimension 4 over finite fields
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(p\)-adic \(L\)-function; Iwasawa theory \(p\)-adic theory, local fields, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Modular and Shimura varieties A note on \(p\)-adic Rankin-Selberg \(L\)-functions
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic \(p\)-adic uniformization; period pairing; \(p\)-adic cohomology theories; abelian schemes; integral models WINTENBERGER (J.-P.) . - Théorème de comparaison p-adique pour les schémas abéliens , I: Construction de l'accouplement de périodes, dans 'Périodes p-adiques' [12], p. 349-397. Zbl 0839.14038 Arithmetic ground fields for abelian varieties, de Rham cohomology and algebraic geometry, Local ground fields in algebraic geometry \(p\)-adic comparison theorem for abelian schemes. I: Construction of period pairings
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass 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; theta functions Analytic theory of abelian varieties; abelian integrals and differentials, Theta functions and abelian varieties On some exceptional cases occuring in the theory of abelian 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 Ehud Hrushovski, Proof of Manin's theorem by reduction to positive characteristic, Model theory and algebraic geometry, Lecture Notes in Math., vol. 1696, Springer, Berlin, 1998, pp. 197 -- 205. Model-theoretic algebra, Arithmetic ground fields for abelian varieties, Abelian varieties of dimension \(> 1\), Model theory (number-theoretic aspects), Classification theory, stability, and related concepts in model theory Proof of Manin's theorem by reduction to positive characteristic
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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 Witt rings of function fields; real analytic manifold; second residue class homomorphism; Artin-Lang property; Witt group of the ring of real analytic functions Algebraic theory of quadratic forms; Witt groups and rings, Real-analytic and semi-analytic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) On Witt rings of function fields of real analytic surfaces and curves
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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 varieties of dimension \(> 1\), Finite ground fields in algebraic geometry, Algebraic moduli of abelian varieties, classification Abelian varieties over finite fields with a specified characteristic polynomial modulo \(\ell\)
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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 \(L\)-functions; modular symbols; \({\mathcal L}\)-invariants; \(p\)-adic integration theory; Darmon cycles; \(p\)-adic Gross-Zagier type formulas Seveso, Marco Adamo, \(p\)-adic \(L\)-functions and the rationality of Darmon cycles, Canad. J. Math., 0008-414X, 64, 5, 1122-1181, (2012) Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Rational points \(p\)-adic \(L\)-functions and the rationality of Darmon cycles
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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 coarse moduli space; semi-stable sheaves; local factoriality for the moduli spaces; rational surface; prioritary sheaves; deformation theory Yoshioka, Kōta, A note on a paper of J.-M. Drézet on the local factoriality of some moduli spaces: ``Points non factoriels des variétés de modules de faisceaux semi-stables sur une surface rationnelle'' [J. Reine Angew. Math. \textbf{413} (1991), 99--126; MR1089799 (92d:14009)], Internat. J. Math., 7, 6, 843-858, (1996) Fine and coarse moduli spaces, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Rational and ruled surfaces A note on a paper of J.-M. Drezet on the local factoriality of some moduli 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 ordered rings with involution; \(C^*\)-algebras and their representations; noncommutative convexity theory; real algebraic geometry Jakob Cimprič, A representation theorem for Archimedean quadratic modules on *-rings, Canad. Math. Bull. 52 (2009), no. 1, 39 -- 52. Topological and ordered rings and modules, General theory of \(C^*\)-algebras, Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Semialgebraic sets and related spaces, Rings with involution; Lie, Jordan and other nonassociative structures A representation theorem for Archimedean quadratic modules on *-rings.
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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 characterization of projective space; ample line bundle Wahl, J. M., A cohomological characterization of \textbf{P}\textit{n}, Invent. Math., 72, 2, 315-322, (1983) Analytic sheaves and cohomology groups, Holomorphic bundles and generalizations A cohomological characterization of \({\mathbb{P}}^ n\)
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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 multiplicity; spectrum of a quasi-unmixed local Nagata ring; embedding dimension; standard bases; tangent cones Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Multiplicity theory and related topics, Relevant commutative algebra On equimultiple subschemes of a local scheme over a field of characteristic zero
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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 multiple zeta values; Furusho conjecture Arithmetic theory of algebraic function fields, Transcendence theory of Drinfel'd and \(t\)-modules, Generalizations (algebraic spaces, stacks), Formal groups, \(p\)-divisible groups, Finite ground fields in algebraic geometry On a conjecture of Furusho 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 good reduction of a curve; Fontaine's rings; crystalline site; unipotent fundamental group F.~Andreatta, A.~Iovita, and M.~Kim, \emph{A \(p\)-adic non-abelian criterion for good reduction of curves}, Duke Math. J. \textbf{164} (2015), no.~13, 2597--2642. DOI 10.1215/00127094-3146817; zbl 1347.11051; MR3405595 Curves over finite and local fields, \(p\)-adic cohomology, crystalline cohomology, Rigid analytic geometry, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) A \(p\)-adic nonabelian criterion for good reduction 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 good towers; graphs Beelen, Peter; Garcia, Arnaldo; Stichtenoth, Henning, On towers of function fields over finite fields.Arithmetic, geometry and coding theory (AGCT 2003), Sémin. Congr. 11, 1-20, (2005), Soc. Math. France, Paris Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Curves over finite and local fields, Rational points On towers 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 singular foliations; codimension 1 foliations; Kupka component; complete intersection; unstable vector bundle; rank 2 vector bundle; splitting of a vector bundle; meromorphic first integral; Barth-Lefschetz theorems Ballico, E., \textit{A splitting theorem for the kupka component of a foliation of} CP\^{}\{n\}, \(n\) \(###\) 6. \textit{addendum to a paper by calvo-andrade and soares}, Ann. Inst. Fourier, 45, 1119-1121, (1995) Dynamical aspects of holomorphic foliations and vector fields, Singularities of holomorphic vector fields and foliations, Complete intersections, Characteristic classes and numbers in differential topology A splitting theorem for the Kupka component of a foliation of \({\mathbb{C}} {\mathbb{P}}^ n, n\geq 6\). Addendum to a paper by O. Calvo-Andrade and M. Soares
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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 Jacobians varieties of modular curves; p-divisible group; Eisenstein ideal S. Kamienny, On \(J_1(p)\) and the kernel of the Eisenstein ideal, J. Reine Angew. Math., 404 (1990), 203-208. Modular and Shimura varieties, Formal groups, \(p\)-divisible groups, Jacobians, Prym varieties On \(J_ 1(p)\) and the kernel of the Eisenstein ideal
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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 characteristic two; instantons DOI: 10.1023/A:1001701428095 Finite ground fields in algebraic geometry, Algebraic moduli problems, moduli of vector bundles Mathematical instantons in characteristic 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 \(b\)-functions; prehomogeneous vector spaces; character sheaves Prehomogeneous vector spaces, Homogeneous spaces and generalizations, Representation theory for linear algebraic groups \(b\)-functions of the prehomogeneous vector space arising from a cuspidal character sheaf of \(E_7\)
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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 semistable sheaf; Bogomolov-Gieseker inequality; positive characteristic Atsushi Moriwaki, A note on Bogomolov-Gieseker's inequality in positive characteristic, Duke Math. J. 64 (1991), no. 2, 361 -- 375. Characteristic classes and numbers in differential topology, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Finite ground fields in algebraic geometry A note on Bogomolov-Gieseker's inequality in positive characteristic
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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 Artin's braid group; representation as subgroup of the symplectic group of \(2g\) by \(2g\) matrices with integral element W. Magnus and A. Peluso, On a theorem of V. I. Arnol'd, Comm. Pure Appl. Math. 22 (1969), 683-692. Braid groups; Artin groups, Riemann surfaces, Coverings of curves, fundamental group On a theorem of V. I. Arnol'd
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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 characteristic p; semigroup of the curve; gaps Bedoya, H.; Stöhr, K. -O.: An algorithm to calculate discrete invariants of singular primes in function fields. J. number theory 27, 310-323 (1987) Singularities of curves, local rings, Arithmetic theory of algebraic function fields An algorithm to calculate discrete invariants of singular primes 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 arithmetic varieties; polarized dynamical system; Dirichlet unit theorem; adelic arithmetic divisors Chen, Huayi; Moriwaki, Atsushi, Algebraic Dynamical Systems and Dirichlet's Unit Theorem on Arithmetic Varieties, Int. Math. Res. Not. IMRN, 1073-7928, 24, 13669-13716, (2015) Arithmetic varieties and schemes; Arakelov theory; heights, Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems, Heights Algebraic dynamical systems and Dirichlet's unit theorem on arithmetic 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 singular varieties; Baum-Fulton-MacPherson's Riemann-Roch theorem; characteristic class DOI: 10.2977/prims/1195166426 Riemann-Roch theorems, Singularities in algebraic geometry, Characteristic classes and numbers in differential topology An extension of Baum-Fulton-MacPherson's Riemann-Roch theorem for singular 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 elliptic curve; obstruction group for realizing characters; Brauer group; Galois cohomology; unramified Brauer group; reciprocity law; hyperelliptic curves Brauer groups of schemes, Elliptic curves Brauer groups of curves and reciprocity laws in Brauer groups of their 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 rings of differential operators and their modules; characteristic \(p\) methods Kontsevich, M, Holonomic \(D\)-modules and positive characteristic, Jpn. J. Math., 4, 1-25, (2009) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Sheaves of differential operators and their modules, \(D\)-modules, Commutative rings of differential operators and their modules, Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure Holonomic \(\mathcal D\)-modules and positive characteristic
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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 Néron-Tate height; p-adic Birch-Swinnerton-Dyer conjecture; Tate-Shafarevich group; elliptic curve; p-adic L-function Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Special algebraic curves and curves of low genus, Local ground fields in algebraic geometry, Elliptic curves, Arithmetic ground fields for abelian varieties, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Heights, Zeta functions and \(L\)-functions On the Birch-Swinnerton-Dyer conjecture mod \(p\)
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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 characteristic \(p\); unirational complete intersections of general type Complete intersections, Rational and unirational varieties A generalization of Morin-Predonzan's theorem on the unirationality of complete intersections
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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 prehomogeneous vector spaces; characteristic 2 Chen, Z, A classification of irreducible prehomogeneous vector spaces over an algebraically closed field of characteristic 2, Acta Math. Sinica, 2, 168-177, (1986) Homogeneous spaces and generalizations, Linear algebraic groups over arbitrary fields A classification of irreducible prehomogeneous vector spaces over an algebraically closed field of characteristic 2. I
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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 dynamical Mordell-Lang conjecture in positive characteristic; classical Mordell-Lang conjecture Arithmetic dynamics on general algebraic varieties, Positive characteristic ground fields in algebraic geometry A fusion variant of the classical and dynamical Mordell-Lang conjectures in positive characteristic
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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 finite field; finite group of automorphisms; Artin L-function; total degree Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry On the degree of Artin \(L\)-functions in characteristic \(p\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic duality theorem of Galois cohomology groups related to abelian varieties; higher dimensional local fields; Weil-Barsotti formula; higher Tate duality Yoshihiro Koya. On a duality theorem of abelian varieties over higher dimensional local fields. {\em Kodai Math. J.}, 2:297--308, 2000 Local ground fields in algebraic geometry, Arithmetic ground fields for abelian varieties, Abelian varieties of dimension \(> 1\), Class field theory; \(p\)-adic formal groups On a duality theorem for abelian varieties over higher dimensional local 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 Hodge theory; \(L\)-values; \(L\)-functions of motives; Euler systems; cyclotomic units; elliptic units; Gauß sums; Heegner points; Beilinson's conjectures Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic aspects of modular and Shimura varieties, \(p\)-adic cohomology, crystalline cohomology, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Generalizations (algebraic spaces, stacks), Units and factorization Values of \(L\)-functions and \(p\)-adic cohomology
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Group schemes, Galois cohomology Degeneration of the Kummer sequence in characteristic \(p>0\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Hilbert's tenth Problem; Undecidability; Elliptic curves; Quadratic forms; Rational points; Diophantine model Eisenträger, K., Hilbert's tenth problem for function fields of varieties over number fields and p-adic fields, J. Algebra, 310, 775-792, (2007) Decidability (number-theoretic aspects), Basic properties of first-order languages and structures, Rational points, Arithmetic theory of algebraic function fields Hilbert's Tenth problem for function fields of varieties over number fields and \(p\)-adic 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 Birch-Swinnerton-Dyer conjecture; complex multiplication \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Elliptic curves On the \(p\)-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication by the ring of integers of \(\mathbb{Q}(\sqrt{-3})\)
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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 Satoshi Kondo & Seidai Yasuda, ``The Riemann-Roch theorem without denominators in motivic homotopy theory'', J. Pure Appl. Algebra218 (2014) no. 8, p. 1478-1495 Riemann-Roch theorems, Chern characters, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Motivic cohomology; motivic homotopy theory, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Riemann-Roch theorems The Riemann-Roch theorem without denominators in motivic homotopy 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 uniform abc conjecture; effective abc conjecture; restricted abc conjecture; Fermat curve; Belyi function Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Linear Diophantine equations, Diophantine inequalities, Rational points, Arithmetic varieties and schemes; Arakelov theory; heights Two restricted ABC conjectures
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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 Deligne cohomology; motivic cohomology; Arakelov intersection theory; arithmetic schemes Arithmetic varieties and schemes; Arakelov theory; heights, Zeta and \(L\)-functions in characteristic \(p\) Deninger's conjectures and Weil-Arakelov cohomology
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