Arithmetic Geometry - Cornell Gary

. .

Résumé :
This book is the result of a conference on arithmetic geometry, held July 30 through August 10, 1984 at the University of Connecticut at Storrs, the purpose of which was to provide a coherent overview of the subject. This subject has enjoyed a resurgence in popularity due in part to Faltings' proof of Mordell's conjecture. Included are extended versions of almost all of the instructional lectures and, in addition, a translation into English of Faltings' ground-breaking paper. ARITHMETIC GEOMETRY should be of great use to students wishing to enter this field, as well as those already working in it. This revised second printing now includes a comprehensive index.

Sommaire:
1: Some Historical Notes. Gerd Faltings. 2: Finiteness Theorems for Abelian Varieties over Number Fields. Gerd Faltings. 3: Group Schemes, Formal Groups, and p-Divisible Groups. Stephen S. Shatz. 4: Abelian Varieties over C. Michael Rosen. 5: Abelian Varieties. J.S. Milne. 6: The Theory of Height Functions. Joseph H. Silverman. 7: Jocobian Varieties. J.S. Milne. 8: Neron Models. M. Artin. 9: Siegel Moduli Schemes and Their Compactifications over C. Ching-Li Chae. 10: Heights and Elliptic Curves. Joseph H. Silverman. 11: Lipman's Proof of Resolution of Singularities for Surfaces. M. Artin. 12: An Introduction to Arakelov Intersection Theory. T. Chinburg. 13: Minimal Models for Curves over Dedekind Rings. T. Chinburg. 14: Local Heights on Curves. Benedict H. Gross. 15: A Higher Dimensional Mordell Conjecture. Paul Vojta.