Geometric Methods in Algebra and Number Theory

• 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

Contenu

• 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 André-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