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Diophantine Approximation and Abelian Varieties

Introductory Lectures

  • Conference proceedings
  • © 1993

Overview

Editors:
  1. Bas Edixhoven

    1. Institut Mathématique, Université de Rennes I, Rennes Cedex, France

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  2. Jan-Hendrik Evertse

    1. Wiskunde en Informatica, Universiteit Leiden, Leiden, The Netherlands

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1566)

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About this book

The 13 chapters of this book centre around the proof of Theorem 1 of Faltings' paper "Diophantine approximation on abelian varieties", Ann. Math.133 (1991) and together give an approach to the proof that is accessible to Ph.D-level students in number theory and algebraic geometry. Each chapter is based on an instructional lecture given by its author ata special conference for graduate students, on the topic of Faltings' paper.

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Table of contents (13 papers)

  1. Front Matter

    Pages i-xiii
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  2. Diophantine Equations and Approximation

    • Frits Beukers
    Pages 1-11

  3. Diophantine Approximation and its Applications

    • Rob Tijdeman
    Pages 13-20

  4. Roth’s Theorem

    • Rob Tijdeman
    Pages 21-30

  5. The Subspace Theorem of W.M. Schmidt

    • Jan-Hendrik Evertse
    Pages 31-50

  6. Heights on Abelian Varieties

    • Johan Huisman
    Pages 51-61

  7. D. Mumford’s “A Remark on Mordell’s Conjecture”

    • Jaap Top
    Pages 63-67

  8. Ample Line Bundles and Intersection Theory

    • Johan de Jong
    Pages 69-76

  9. The Product Theorem

    • Marius van der Put
    Pages 77-82

  10. Geometric Part of Faltings’s Proof

    • Carel Faber
    Pages 83-91

  11. Faltings’s Version of Siegel’s Lemma

    • Robert-Jan Kooman
    Pages 93-96

  12. Arithmetic Part of Faltings’s Proof

    • Bas Edixhoven
    Pages 97-110

  13. Points of Degree d on Curves over Number Fields

    • Gerard van der Geer
    Pages 111-116

  14. “The” General Case of S. Lang’s Conjecture (after Faltings)

    • Frans Oort
    Pages 117-122

  15. Back Matter

    Pages 123-127
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Editors and Affiliations

  • Institut Mathématique, Université de Rennes I, Rennes Cedex, France

    Bas Edixhoven

  • Wiskunde en Informatica, Universiteit Leiden, Leiden, The Netherlands

    Jan-Hendrik Evertse

Bibliographic Information

  • Book Title: Diophantine Approximation and Abelian Varieties

  • Book Subtitle: Introductory Lectures

  • Editors: Bas Edixhoven, Jan-Hendrik Evertse

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-48208-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-540-57528-3Published: 20 December 1993

  • eBook ISBN: 978-3-540-48208-6Published: 05 February 2009

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 130

  • Topics: Number Theory, Algebraic Geometry

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