Ebook: Diophantine Approximation and Abelian Varieties

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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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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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.
Content:
Front Matter....Pages i-xiii
Diophantine Equations and Approximation....Pages 1-11
Diophantine Approximation and its Applications....Pages 13-20
Roth’s Theorem....Pages 21-30
The Subspace Theorem of W.M. Schmidt....Pages 31-50
Heights on Abelian Varieties....Pages 51-61
D. Mumford’s “A Remark on Mordell’s Conjecture”....Pages 63-67
Ample Line Bundles and Intersection Theory....Pages 69-76
The Product Theorem....Pages 77-82
Geometric Part of Faltings’s Proof....Pages 83-91
Faltings’s Version of Siegel’s Lemma....Pages 93-96
Arithmetic Part of Faltings’s Proof....Pages 97-110
Points of Degree d on Curves over Number Fields....Pages 111-116
“The” General Case of S. Lang’s Conjecture (after Faltings)....Pages 117-122
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.
Content:
Front Matter....Pages i-xiii
Diophantine Equations and Approximation....Pages 1-11
Diophantine Approximation and its Applications....Pages 13-20
Roth’s Theorem....Pages 21-30
The Subspace Theorem of W.M. Schmidt....Pages 31-50
Heights on Abelian Varieties....Pages 51-61
D. Mumford’s “A Remark on Mordell’s Conjecture”....Pages 63-67
Ample Line Bundles and Intersection Theory....Pages 69-76
The Product Theorem....Pages 77-82
Geometric Part of Faltings’s Proof....Pages 83-91
Faltings’s Version of Siegel’s Lemma....Pages 93-96
Arithmetic Part of Faltings’s Proof....Pages 97-110
Points of Degree d on Curves over Number Fields....Pages 111-116
“The” General Case of S. Lang’s Conjecture (after Faltings)....Pages 117-122
Back Matter....Pages 123-127
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