Title	Diophantine Approximation and Abelian Varieties [electronic resource] / edited by Bas Edixhoven, Jan-Hendrik Evertse
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1993
Connect to	http://dx.doi.org/10.1007/978-3-540-48208-6
Descript	XIV, 130 p. online resource

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

Diophantine Equations and Approximation -- Diophantine Approximation and its Applications -- Rothโs Theorem -- The Subspace Theorem of W.M. Schmidt -- Heights on Abelian Varieties -- D. Mumfordโs โA Remark on Mordellโs Conjectureโ -- Ample Line Bundles and Intersection Theory -- The Product Theorem -- Geometric Part of Faltingsโs Proof -- Faltingsโs Version of Siegelโs Lemma -- Arithmetic Part of Faltingsโs Proof -- Points of Degree d on Curves over Number Fields -- โTheโ General Case of S. Langโs Conjecture (after Faltings)

1. Mathematics
2. Algebraic geometry
3. Number theory
4. Mathematics
5. Number Theory
6. Algebraic Geometry