Geometric methods in algebra and number theory


Geometric methods in algebra and number theory

Fedor Bogomolov, Yuri Tschinkel, editors

(Progress in mathematics, v. 235)

Birkhäuser, c2005

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Includes bibliographical references



* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry


* Preface * Bauer/Catanese/Grunewald: Beauville surfaces without real structures * Bogomolov/Tschinkel: Couniformization of curves over number fields * Budur: On the V-filtration of D-modules * Chai: Hecke orbits on Siegel modular varieties * Cluckers/Loeser: Ax-Kochen-Ersov Theorems for p-adic integrals and motivic integration * De Concini/Procesi: Nested sets and Jeffrey-Kirwan residues * Ellenberg/Venkatesh: Counting extensions of function fields with bounded discriminant and specified Galois group * Hassett: Classical and minimal models of the moduli space of curves of genus two * Hausel: Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve * Pineiro/Szpiro/Tucker: Mahler measure for dynamical systems on P1 and intersection theory on a singular arithmetic surface * Pink: A Combination of the Conjecture of Mordell-Lang and Andre-Oort * Spitzweck: Motivic approach to limit sheaves * Swinnerton-Dyer: Counting points on cubic surfaces, II * Tamvakis: Quantum cohomology of isotropic Grassmannians * Zarhin: Endomorphism algebras of superelliptic Jacobians

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