Beschreibung
This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation.
Inhaltsverzeichnis
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.
