Diophantine Approximation and Abelian Varieties

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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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.

• Abelian Varieties
• Abelian variety
• Diophantine approximation
• Grad
• algebraic geometry
• number theory

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

  Bas Edixhoven

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

  Jan-Hendrik Evertse

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