Rational Points: Seminar Bonn/Wuppertal 1983/84 (Aspects of Mathematics (6))

This book consists of the notes from the seminar Bonn/ Wuppertal 1983/ 84 on Arithmetic Geometry. It contains a proof for the Mordell conjecture and may be useful as an introduction to Arakelov's point of view in diophantine geometry. The third edition includes an appendix in which a detailed survey on the spectacular recent developments in arithmetic algebraic geometry is given. These beautiful new results have their roots in the material covered by this book. Front Matter....Pages i-xi Moduli Spaces....Pages 1-32 Heights....Pages 33-52 Some Facts from the Theory of Group Schemes....Pages 53-113 Tate’s Conjecture on the Endomorphisms of Abelian Varieties....Pages 114-153 The Finiteness Theorems of Faltings....Pages 154-202 Complements to Mordell....Pages 203-227 Intersection Theory on Arithmetic Surfaces....Pages 228-268 Back Matter....Pages 269-312