Galois Representations in Arithmetic Algebraic Geometry

doi:10.1017/CBO9780511662010

This book contains conference proceedings from 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 which have received substantial attention, e.g. 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. Others are research papers by authors such as Coleman and Mazur, Goncharov, Gross and Serre.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-vii
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List of participants
pp viii-viii
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Lecture programme
pp ix-x
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1 - The Eigencurve
pp 1-114
- By R. Coleman, B. Mazur
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2 - Geometric trends in Galois module theory
pp 115-146
- By Boas Erez
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3 - Mixed elliptic motives
pp 147-222
- By Alexander Goncharov
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4 - On the Satake isomorphism
pp 223-238
- By Benedict H. Gross
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5 - Open problems regarding rational points on curves and varieties
pp 239-266
- By B. Mazur
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6 - Models of Shimura varieties in mixed characteristics
pp 267-350
- By Ben Moonen
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7 - Euler systems and modular elliptic curves
pp 351-368
- By Karl Rubin
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8 - Basic notions of rigid analytic geometry
pp 369-378
- By Peter Schneider
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9 - An introduction to Kato's Euler systems
pp 379-460
- By A. J. Scholl
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10 - La distribution d'Euler-Poincaré d'un groupe profini
pp 461-493
- By Jean-Pierre Serre
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Galois Representations in Arithmetic Algebraic Geometry

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-vii

List of participants
pp viii-viii

Lecture programme
pp ix-x

1 - The Eigencurve
pp 1-114

2 - Geometric trends in Galois module theory
pp 115-146

3 - Mixed elliptic motives
pp 147-222

4 - On the Satake isomorphism
pp 223-238

5 - Open problems regarding rational points on curves and varieties
pp 239-266

6 - Models of Shimura varieties in mixed characteristics
pp 267-350

7 - Euler systems and modular elliptic curves
pp 351-368

8 - Basic notions of rigid analytic geometry
pp 369-378

9 - An introduction to Kato's Euler systems
pp 379-460

10 - La distribution d'Euler-Poincaré d'un groupe profini
pp 461-493

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Galois Representations in Arithmetic Algebraic Geometry

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