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Birkhäuser

Geometric Methods in Algebra and Number Theory

  • Textbook
  • © 2005

Overview

Editors:
  1. Fedor Bogomolov

    1. Department of Mathematics Courant Institute of Mathematical Sciences, New York University, New York, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Yuri Tschinkel

    1. Department of Mathematics, Princeton University, Princeton, USA

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    You can also search for this editor in PubMed   Google Scholar

  • 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

Part of the book series: Progress in Mathematics (PM, volume 235)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Beauville surfaces without real structures

    • Ingrid Bauer, Fabrizio Catanese, Fritz Grunewald
    Pages 1-42

  3. Couniformization of curves over number fields

    • Fedor Bogomolov, Yuri Tschinkel
    Pages 43-57

  4. On the V-filtration of \(D\)-modules

    • Nero Budur
    Pages 59-70

  5. Hecke orbits on Siegel modular varieties

    • Ching-Li Chai
    Pages 71-107

  6. Ax-Kochen-Eršov Theorems for p-adic integrals and motivic integration

    • Raf Cluckers, François Loeser
    Pages 109-137

  7. Nested sets and Jeffrey-Kirwan residues

    • Corrado De Concini, Claudio Procesi
    Pages 139-149

  8. Counting extensions of function fields with bounded discriminant and specified Galois group

    • Jordan S. Ellenberg, Akshay Venkatesh
    Pages 151-168

  9. Classical and minimal models of the moduli space of curves of genus two

    • Brendan Hassett
    Pages 169-192

  10. Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve

    • Tamás Hausel
    Pages 193-217

  11. Mahler measure for dynamical systems on ℙ1 and intersection theory on a singular arithmetic surface

    • Jorge Pineiro, Lucien Szpiro, Thomas J. Tucker
    Pages 219-250

  12. A Combination of the Conjectures of Mordell-Lang and André-Oort

    • Richard Pink
    Pages 251-282

  13. Motivic approach to limit sheaves

    • Markus Spitzweck
    Pages 283-302

  14. Counting points on cubic surfaces, II

    • Peter Swinnerton-Dyer
    Pages 303-309

  15. Quantum cohomology of isotropic Grassmannians

    • Harry Tamvakis
    Pages 311-338

  16. Endomorphism algebras of superelliptic jacobians

    • Yuri G. Zarhin
    Pages 339-362
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Keywords

Reviews

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)

Editors and Affiliations

  • Department of Mathematics Courant Institute of Mathematical Sciences, New York University, New York, USA

    Fedor Bogomolov

  • Department of Mathematics, Princeton University, Princeton, USA

    Yuri Tschinkel

Bibliographic Information

  • Book Title: Geometric Methods in Algebra and Number Theory

  • Editors: Fedor Bogomolov, Yuri Tschinkel

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/b138649

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Birkhäuser Boston 2005

  • Hardcover ISBN: 978-0-8176-4349-2Published: 12 November 2004

  • eBook ISBN: 978-0-8176-4417-8Published: 22 June 2006

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: VIII, 362

  • Number of Illustrations: 6 b/w illustrations

  • Topics: Algebra, Algebraic Geometry, Number Theory, Geometry

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