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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Elliptic curves over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Special algebraic curves and curves of low genus, Elliptic curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields A. Moriwaki, Continuity of volumes on arithmetic varieties, J. Algebraic Geom. 18 (2009), no. 3, 407-457. Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic ground fields for curves, Global theory and resolution of singularities (algebro-geometric aspects), Special algebraic curves and curves of low genus, Global ground fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Singularities of surfaces or higher-dimensional varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, Local ground fields in algebraic geometry, Galois cohomology
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Masser, D. W.; Wüstholz, G.: Refinements of the Tate conjecture for abelian varieties. Abelian varieties (Egloffstein, 1993), 211-223 (1995) Arithmetic ground fields for abelian varieties, Global ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields González-Jiménez, E.; Xarles, X., On symmetric square values of quadratic polynomials, Acta Arith., 149, 2, 145-159, (2011) Counting solutions of Diophantine equations, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Harry Tamvakis, Schubert polynomials and Arakelov theory of orthogonal flag varieties, Math. Z. 268 (2011), no. 1-2, 355 -- 370. Grassmannians, Schubert varieties, flag manifolds, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields A. Moriwaki, Bogomolov conjecture over function fields for stable curves with only irreducible fibers, Compos. Math. 105 (1997), 125-140. Algebraic functions and function fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Picard groups
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Geer, G; Katsura, T, On a stratification of the moduli of \(K3\) surfaces, J. Eur. Math. Soc., 2, 259-290, (2000) \(K3\) surfaces and Enriques surfaces, Families, moduli, classification: algebraic theory, Arithmetic varieties and schemes; Arakelov theory; heights, Finite ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Leveque, W. J.: Rational points on curves of genus greater than 1. J. reine angew math. 206, 45-52 (1961) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Heights, Quadratic and bilinear Diophantine equations, Rational points, Plane and space curves, Linear algebraic groups over global fields and their integers
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Jürgen Jost and Shing-Tung Yau, Applications of quasilinear PDE to algebraic geometry and arithmetic lattices, Algebraic geometry and related topics (Inchon, 1992) Conf. Proc. Lecture Notes Algebraic Geom., I, Int. Press, Cambridge, MA, 1993, pp. 169 -- 193. Global Riemannian geometry, including pinching, Arithmetic varieties and schemes; Arakelov theory; heights, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Harmonic maps, etc., Global differential geometry of Hermitian and Kählerian manifolds, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Differential geometry of symmetric spaces, Research exposition (monographs, survey articles) pertaining to differential geometry, Research exposition (monographs, survey articles) pertaining to global analysis
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields [23] Kawaguchi (S.) and Moriwaki (A.).-- Inequalities for semistable families of arithmetic varieties, J. Math. Kyoto Univ. 41 (2001), no.~1, 97-182. &MR~18 | &Zbl~1041. Arithmetic varieties and schemes; Arakelov theory; heights, (Equivariant) Chow groups and rings; motives, Topological properties in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arledge, J., \textit{S}-units attached to genus 3 hyperelliptic curves, J. Number Theory, 63, 12-29, (1997) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields L.-C. Hsia, On the dynamical height zeta functions , J. Number Theory 63 (1997), 146--169. Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic varieties and schemes; Arakelov theory; heights, Tauberian theorems
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Corvaja, P.; Zannier, U., On the number of integral points on algebraic curves, Journal für die reine und angewandte Mathematik, 565, 27-42, (2003) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Diophantine inequalities, Global ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Harbater, D.: Arithmetic discriminants and horizontal intersections. Mathematische annalen 291, 705-724 (1991) Arithmetic varieties and schemes; Arakelov theory; heights, Divisors, linear systems, invertible sheaves, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Global ground fields in algebraic geometry, Local ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields J.L. Thunder, Points of bounded height on Schubert varieties , Inter. J. Number Theory, Heights, Varieties over global fields, Grassmannians, Schubert varieties, flag manifolds
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Kim, Minhyong; Thakur, Dinesh S.; Voloch, José Felipe, Diophantine approximation and deformation, Bull. Soc. Math. France, 128, 4, 585-598, (2000) Approximation in non-Archimedean valuations, Approximation to algebraic numbers, Arithmetic ground fields (finite, local, global) and families or fibrations, Heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Rational points, Varieties over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Bruin, N, The arithmetic of Prym varieties in genus 3, Compos. Math, 144, 317-338, (2008) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Arithmetic ground fields for curves, Algebraic theory of abelian varieties, Research exposition (monographs, survey articles) pertaining to number theory
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields [Mo] A. Moriwaki,Inequality of Bogolomov-Gieseker type on arithmetic surfaces, Duke Math. J.74 (1994), 713--761 Arithmetic varieties and schemes; Arakelov theory; heights, Topological properties in algebraic geometry, Characteristic classes and numbers in differential topology
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields A. Schmidt, ''Extensions with restricted ramification and duality for arithmetic schemes,'' Compositio Math., vol. 100, iss. 2, pp. 233-245, 1996. Arithmetic varieties and schemes; Arakelov theory; heights, Homotopy theory and fundamental groups in algebraic geometry, Other abelian and metabelian extensions
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields C. Gasbarri, Hauteurs canoniques sur l'espace de modules des fibrés stables sur une courbe algébrique , Bull. Soc. Math. France 125 (1997), 457--491. Arithmetic varieties and schemes; Arakelov theory; heights, Families, moduli of curves (algebraic), Algebraic moduli problems, moduli of vector bundles
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields N. Broberg, Rational points on finite covers of \(\mathbb P^1\) and \(\mathbb P^2\) , J. Number Theor. 101 (2003), 195-207. Rational points, Coverings of curves, fundamental group, Coverings in algebraic geometry, Varieties over global fields, Heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Proceedings, conferences, collections, etc. pertaining to number theory, Arithmetic algebraic geometry (Diophantine geometry), Algebraic coding theory; cryptography (number-theoretic aspects), Jacobians, Prym varieties, Arithmetic varieties and schemes; Arakelov theory; heights, Proceedings of conferences of miscellaneous specific interest
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields T. Lange. Montgomery Addition for Genus Two Curves. In Algorithmic Number Theory Seminar ANTS-VI, volume 3076 of Lect. Notes Comput. Sci., pages 309-317, 2004. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Applications to coding theory and cryptography of arithmetic geometry, Cryptography
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, Group actions on varieties or schemes (quotients), \(K\)-theory of schemes, Relations of \(K\)-theory with cohomology theories
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Derksen, H.; Masser, D., Linear equations over multiplicative groups, recurrences, and mixing I, Proc. Lond. Math. Soc. (3), 104, 5, 1045-1083, (2012) Heights, Global ground fields in algebraic geometry, Linear Diophantine equations, Diophantine equations in many variables, Varieties over global fields
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Elliptic curves over global fields, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Quadratic and bilinear Diophantine equations
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Q.V. Pham. Zur Rolle der Chern-Klassen in der Arakelovschen arithmetischen Geometrie. Thesis 1992. Univ. Hamburg. Arithmetic varieties and schemes; Arakelov theory; heights, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Characteristic classes and numbers in differential topology
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields N. Bruin, M. Stoll,The Mordell-Weil sieve: Proving non-existence of rational points on curves, LMS J. Comput. Math. 13 (2010), 272-306. MR2685127 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computer solution of Diophantine equations, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields A. Abbes, Cycles on arithmetic surfaces, Compos. Math., 122 (2000), 23--111. Arithmetic varieties and schemes; Arakelov theory; heights, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Algebraic cycles, Étale and other Grothendieck topologies and (co)homologies
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Waldschmidt M.: Density measure of rational points on abelian varieties. Nagoya Math. J. 155, 27--53 (1999) Abelian varieties of dimension \(> 1\), Rational points, Transcendence theory of elliptic and abelian functions, Arithmetic ground fields for abelian varieties, Heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms, Relationship to Lie algebras and finite simple groups, Modular and Shimura varieties, Algebraic moduli of abelian varieties, classification, \(K3\) surfaces and Enriques surfaces, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Heights, Complex multiplication and moduli of abelian varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Dongwen Liu 2014 Kato's residue homomorphisms and reciprocity laws on arithmetic surfaces \textit{Adv. Math.}251 1--21 Arithmetic ground fields for curves, \(K\)-theory of local fields, Arithmetic varieties and schemes; Arakelov theory; heights, Higher symbols, Milnor \(K\)-theory
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), Galois cohomology, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, Rational points, Elliptic curves, Elliptic curves over global fields, Finite ground fields in algebraic geometry, Elliptic surfaces, elliptic or Calabi-Yau fibrations
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Arithmetic ground fields for curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Algebraic number theory computations, Computational aspects of algebraic curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Curves over finite and local fields, Coverings of curves, fundamental group, Special algebraic curves and curves of low genus
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Complex multiplication and moduli of abelian varieties, Complex multiplication and abelian varieties, Zeta functions and \(L\)-functions of number fields, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields van Frankenhuijsen, Machiel, \(ABC\) implies the radicalized Vojta height inequality for curves, J. Number Theory, 127, 2, 292-300, (2007) Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Counting solutions of Diophantine equations, Diophantine inequalities, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Hübner, K.: Aspherical neighborhoods on arithmetic surfaces. Ph.D. thesis (2016) Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic algebraic geometry (Diophantine geometry)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Javanpeykar, A, Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized surfaces, Bull. Lond. Math. Soc., 47, 55-64, (2015) Arithmetic ground fields for curves, Families, moduli of curves (algebraic), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Roy D., Invent. Math. 109 pp 547-- (1992) Algebraic number theory: global fields, Global ground fields in algebraic geometry, General properties and structure of real Lie groups, Diophantine approximation, transcendental number theory
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields P. Habegger, A Bogomolov property for curves modulo algebraic subgroups , Bull. Soc. Math. France 137 (2009), 93--125. Heights, Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems, Arithmetic ground fields for curves, Counting solutions of Diophantine equations, Rational points, Global ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields S. Siksek and M. Stoll, Partial descent on hyperelliptic curves and the generalized Fermat equation \(x\)\^{}\{3\} + \(y\)\^{}\{4\} + \(z\)\^{}\{5\} = 0, Bull. London Math. Soc. \textbf{44} (2012), 151-166. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Varieties over global fields, Analytic theory of abelian varieties; abelian integrals and differentials, Divisors, linear systems, invertible sheaves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Jordi Guàrdia, Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves, Ann. Inst. Fourier (Grenoble) 57 (2007), no. 4, 1253 -- 1283 (English, with English and French summaries). Curves of arbitrary genus or genus \(\ne 1\) over global fields, Theta functions and abelian varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Chambert-Loir, A., Théorèmes d'algébricite en géométrie diophantienne (d'après J.-B. bost, Y. André, D. and G. chudnovsky), Asterisque, 282, 175-209, (2002) Varieties over global fields, Transcendence (general theory), Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Chambert-Loir, Antoine; Ducros, Antoine, Formes différentielles réelles et courants sur LES espaces de berkovich, (2012) Elliptic curves, Arithmetic varieties and schemes; Arakelov theory; heights, Abelian varieties of dimension \(> 1\)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic aspects of modular and Shimura varieties, Heights, Arithmetic ground fields for abelian varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Hajli, M., Spectre du laplacien singulier associé aux métriques canoniques sur \(p^1\) et la théorie des séries de Fourier-Bessel généralisée, J. Math. Pure Appl., 103, 2, 429-471, (2015) Spectral problems; spectral geometry; scattering theory on manifolds, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Arithmetic varieties and schemes; Arakelov theory; heights, Estimates of eigenvalues in context of PDEs
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Esnault, Hélène; Viehweg, Eckart, Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields, Compos. Math., 0010-437X, 76, 1-2, 69\textendash 85 pp., (1990) Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for surfaces or higher-dimensional varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Burgos Gil, J.; Kramer, J.; Kühn, U., Cohomological arithmetic Chow rings, J. Inst. Math. Jussieu, 6, 1-172, (2007) Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Elliptic curves over global fields, Dynamical systems on Berkovich spaces, Zeta functions and \(L\)-functions, Arithmetic varieties and schemes; Arakelov theory; heights, Modular correspondences, etc.
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields M. Kaneko and D. Zagier, A generalized Jacobi theta function and quasimodular forms, in \textit{The moduli space of curves (Texel Island, 1994)}, 165--172, Progr. Math., 129, Birkhäuser Boston, Boston, MA, 1995.Zbl 0892.11015 MR 1363056 Holomorphic modular forms of integral weight, Theta functions and abelian varieties, Theta functions and curves; Schottky problem, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Other groups and their modular and automorphic forms (several variables)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Maillot, V; Rössler, D, On the periods of motives with complex multiplication and a conjecture of Gross-Deligne, Ann. Math., 160, 727-754, (2004) Arithmetic varieties and schemes; Arakelov theory; heights, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian varieties, Complex multiplication and abelian varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Elisenda Feliu, Adams operations on higher arithmetic \?-theory, Publ. Res. Inst. Math. Sci. 46 (2010), no. 1, 115 -- 169. Arithmetic varieties and schemes; Arakelov theory; heights, \(K\)-theory of schemes
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Families, moduli of curves (algebraic), Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Geometric invariant theory, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation in probabilistic number theory, Rigid analytic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields M. Hindry, J.H. Silverman, On Lehmer's conjecture for elliptic curves, in Séminaire de Théorie des Nombres, Paris (1988--1989), Progress in Mathematics, Vol. 91, Birkhäuser, Boston, MA, 1990, pp. 103--116. Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic curves, Elliptic curves over global fields
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Ullmo, E.: Points entiers, points de torsion et amplitude arithmétique. Amer J math 117, 1039-1056 (1995) Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic curves, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Girard, M., The group of Weierstrass points of a plane quartic with at least eight hyperflexes, Math. Comp., 75, 1561-1583, (2006) Riemann surfaces; Weierstrass points; gap sequences, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computational aspects of algebraic curves, Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields P. Autissier, Un lemme matriciel effectif , Math. Z. 273 (2013), 355-361. Arithmetic varieties and schemes; Arakelov theory; heights, Abelian varieties of dimension \(> 1\)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Heights, Varieties over global fields, Global ground fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields W. Gubler, K. Künnemann, A tropical approach to non-archimedean Arakelov theory. \textit{Algebra Number Theory} 11 (2017), 77-180. MR3602767 Zbl 06679113 Arithmetic varieties and schemes; Arakelov theory; heights, Rigid analytic geometry, Non-Archimedean analysis
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Bost, Jean-Benoît; Freixas i Montplet, Gerard, Semi-abelian schemes and heights of cycles in moduli spaces of abelian varieties, Rend. Semin. Mat. Univ. Padova, 128, 55-89 (2013), (2012) Arithmetic varieties and schemes; Arakelov theory; heights, Algebraic moduli of abelian varieties, classification
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus, Jacobians, Prym varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, Adèle rings and groups, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Arithmetic ground fields for surfaces or higher-dimensional varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields DOI: 10.4153/CJM-2010-032-0 Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Special algebraic curves and curves of low genus, Curves over finite and local fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Cubic and quartic extensions, Class numbers, class groups, discriminants, Applications to coding theory and cryptography of arithmetic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Deninger, Christopher, On the \(\Gamma \)-factors of motives. II, Doc. Math., 1431-0635, 6, 69-97 (electronic), (2001) \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields José Ignacio Burgos Gil and Elisenda Feliu, Higher arithmetic Chow groups, Comment. Math. Helv. 87 (2012), no. 3, 521 -- 587. Arithmetic varieties and schemes; Arakelov theory; heights, (Equivariant) Chow groups and rings; motives, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Tan S.-L, J. Reine Angew. Math. 461 pp 123-- (1995) Algebraic functions and function fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Quadratic and bilinear Diophantine equations, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Plane and space curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields . Call, G. and Silverman, J. : Computing canonical heights on K3 surfaces , in preparation. \(K3\) surfaces and Enriques surfaces, Arithmetic varieties and schemes; Arakelov theory; heights, Computer solution of Diophantine equations, Computational aspects of algebraic surfaces
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for curves, Algebraic functions and function fields in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computational aspects of algebraic curves, Number-theoretic algorithms; complexity
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Heights, Other Dirichlet series and zeta functions, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Model theory (number-theoretic aspects), Applications of model theory, \(p\)-adic and power series fields, Heights, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields N. Elkies, \(ABC\) implies Mordell, Int. Math. Res. Notices (1991), no. 7, 99--109. Diophantine inequalities, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Measures of irrationality and of transcendence, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Cubic and quartic Diophantine equations, Rational points, Arithmetic ground fields for curves
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic varieties and schemes; Arakelov theory; heights, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Abelian varieties of dimension \(> 1\), Heights, Global ground fields in algebraic geometry, Arithmetic ground fields for abelian varieties
| 0
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic aspects of modular and Shimura varieties, Heights, Rational points
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Kudla, S., Rapoport, M., Yang, T.: Modular Forms and Special Cycles on Shimura Curves. Annals of Math. Studies, vol. 161. Princeton University Press, Princeton (2006) Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Fourier coefficients of automorphic forms, Forms of half-integer weight; nonholomorphic modular forms, Arithmetic varieties and schemes; Arakelov theory; heights
| 0
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields C. Faber , Geometric part of Faltings's proof , In: ''[EE]'', Chapitre IX, pp. 83 - 91 . MR 1289007 | Zbl 0811.14023 Rational points, Arithmetic ground fields for abelian varieties, Arithmetic varieties and schemes; Arakelov theory; heights, Algebraic theory of abelian varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields K. V. Nguyen, On certain Mordell-Weil lattices of hyperelliptic type on rational surfaces, J. Math. Sci. (New York) 102 (2000), no. 2, 3938--3977. Jacobians, Prym varieties, Rational and ruled surfaces, Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Rational and unirational varieties
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Fontaine, J.-M.: Le corps des périodes \(p\)-adiques. With an appendix by Pierre Colmez. Périodes \(p\)-adiques (Bures-sur-Yvette, 1988). Astérisque No. 223, pp. 59-111 (1994) Local ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic curves, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Theta functions and abelian varieties
| 0
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Rational points, Heights, Model theory of ordered structures; o-minimality, Modular and Shimura varieties
| 0
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Galois cohomology of linear algebraic groups, Asymptotic results on counting functions for algebraic and topological structures, Rational points, Global ground fields in algebraic geometry, Jacobians, Prym varieties, Special algebraic curves and curves of low genus
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Complex multiplication and moduli of abelian varieties, Arithmetic aspects of modular and Shimura varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic varieties and schemes; Arakelov theory; heights
| 0
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Vojta, P., \textit{A generalization of theorems of faltings and thue-Siegel-Roth-wirsing}, J. Amer. Math. Soc., 5, 763-804, (1992) Diophantine inequalities, Arithmetic varieties and schemes; Arakelov theory; heights
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Wolfgang M. Schmidt, Heights of algebraic points, Number theory and its applications (Ankara, 1996) Lecture Notes in Pure and Appl. Math., vol. 204, Dekker, New York, 1999, pp. 185 -- 225. Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Diophantine approximation, transcendental number theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Arithmetic ground fields for curves
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