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9780817643492

Geometric Methods in Algebra and Number Theory

by ;
  • ISBN13:

    9780817643492

  • ISBN10:

    0817643494

  • Format: Hardcover
  • Copyright: 2004-12-01
  • Publisher: Birkhauser

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Summary

The transparency and power of geometric constructions has been a source of inspiration to generations of mathematicians. The beauty and persuasion of pictures, communicated in words or drawings, continues to provide the intuition and arguments for working with complicated concepts and structures of modern mathematics. This volume contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory. Key topics include: * Curves and their Jacobians * Algebraic surfaces * Moduli spaces, Shimura varieties * Motives and motivic integration * Number-theoretic applications, rational points * Combinatorial aspects of algebraic geometry * Quantum cohomology * Arithmetic dynamical systems The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry; the text can serve as an intense introduction for graduate students and those wishing to pursue research in these areas. Contributors: I. Bauer, F. Bogomolov, N. Budur, F. Catanese, C.-L. Chai, R. Cluckers, C. De Concini, J.S. Ellenberg, F. Grunewald, B. Hassett, T. Hausel, F. Loeser, J. Pineiro, R. Pink, C. Procesi, M. Spitzweck, P. Swinnerton-Dyer, L. Szpiro, H. Tamvakis, Y. Tschinkel, T.J. Tucker, A. Venkatesh, and Y.G. Zarhin.

Table of Contents

Beauville surfaces without real structuresp. 1
Couniformization of curves over number fieldsp. 43
On the V-filtration of D-modulesp. 59
Hecke orbits on Siegel modular varietiesp. 71
Ax-Kochen-Ersov theorems for p-adic integrals and motivic integrationp. 109
Nested sets and Jeffrey-Kirwan residuesp. 139
Counting extensions of function fields with bounded discriminant and specified Galois groupp. 151
Classical and minimal models of the moduli space of curves of genus twop. 169
Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curvep. 193
Mahler measure for dynamical systems on P[superscript 1] and intersection theory on a singular arithmetic surfacep. 219
A combination of the conjectures of Mordell-Lang and Andre-Oortp. 251
Motivic approach to limit sheavesp. 283
Counting points on cubic surfaces, IIp. 303
Quantum cohomology of isotropic Grassmanniansp. 311
Endomorphism algebras of superelliptic jacobiansp. 339
Table of Contents provided by Blackwell. All Rights Reserved.

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