β Scribed by Frits Beukers (auth.), Bas Edixhoven, Jan-Hendrik Evertse (eds.)
No coin nor oath required. For personal study only.
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.
Front Matter....Pages i-xiii
Diophantine Equations and Approximation....Pages 1-11
Diophantine Approximation and its Applications....Pages 13-20
Rothβs Theorem....Pages 21-30
The Subspace Theorem of W.M. Schmidt....Pages 31-50
Heights on Abelian Varieties....Pages 51-61
D. Mumfordβs βA Remark on Mordellβs Conjectureβ....Pages 63-67
Ample Line Bundles and Intersection Theory....Pages 69-76
The Product Theorem....Pages 77-82
Geometric Part of Faltingsβs Proof....Pages 83-91
Faltingsβs Version of Siegelβs Lemma....Pages 93-96
Arithmetic Part of Faltingsβs Proof....Pages 97-110
Points of Degree d on Curves over Number Fields....Pages 111-116
βTheβ General Case of S. Langβs Conjecture (after Faltings)....Pages 117-122
Back Matter....Pages 123-127
Number Theory; Algebraic Geometry
π SIMILAR VOLUMES
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 ba
<p>"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In p
This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus - a person whose very existence has long been doubted
The first part of the book presents the elementary facts of algebraic geometry essential to understanding the rest of it. The second half of the book considers the evolution of the theory of Diophantine equations from the Renaissance to the middle of the 20th century. In particular, the book include