Galois Representations in Arithmetic Algebraic Geometry

ISBN-13: 9780521644198 / Angielski / Miękka / 1999 / 504 str.

A. J. Scholl; Richard Lawrence Taylor; R. L. Taylor

Opis

This book is a conference proceedings based on the 1996 Durham Symposium on "Galois representations in arithmetic algebraic geometry." The title was interpreted loosely and the symposium covered recent developments on the interface between algebraic number theory and arithmetic algebraic geometry. The book reflects this and contains a mixture of articles. Some are expositions of subjects that have received substantial recent attention: Erez on geometric trends in Galois module theory; Mazur on rational points on curves and varieties; Moonen on Shimura varieties in mixed characteristics; Rubin and Scholl on the work of Kato on the Birch-Swinnerton-Dyer conjecture; and Schneider on rigid geometry. Some are research papers by: Coleman and Mazur, Goncharov, Gross, Serre.

Spis treści

Preface; List of participants; Lecture programme; 1. The Eigencurve R. Coleman and B. Mazur; 2. Geometric trends in Galois module theory Boas Erez; 3. Mixed elliptic motives Alexander Goncharov; 4. On the Satake isomorphism Benedict H. Gross; 5. Open problems regarding rational points on curves and varieties B. Mazur; 6. Models of Shimura varieties in mixed characteristics Ben Moonen; 7. Euler systems and modular elliptic curves Karl Rubin; 8. Basic notions of rigid analytic geometry Peter Schneider; 9. An introduction to Kato's Euler systems A. J. Scholl; 10. La distribution d'Euler-Poincaré d'un groupe profini Jean-Pierre Serre.