Geometric Methods in Algebra and Number Theory

ISBN-13: 9780817643492 / Angielski / Twarda / 2004 / 362 str.

Fedor Bogomolov; Yuri Tschinkel

Opis

* 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

Recenzje

From the reviews:

"This is a collection of articles on algebraic and arithmetic geometry most of which were presented at a conference that took place in Miami in December 2003. ... this volume will be attractive for researchers and graduate students in arithmetic geometry. The surveys provided can serve as an introduction for them and offer guidance for further study." (Ch. Baxa, Monatshefte für Mathematik, Vol. 152 (1), September, 2007)

Spis treści

* 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–Eršov 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