Euler systems / by Karl Rubin.

Format:

Book

Author/Creator:

Rubin, Karl, author.

Contributor:

Rubin, Karl, Contributor.

Series:

Annals of mathematics studies ; Number 147.

Annals of Mathematics Studies ; Number 147

Language:

English

Subjects (All):

Algebraic number theory.

p-adic numbers.

Physical Description:

1 online resource (241 p.)

Edition:

1st ed.

Place of Publication:

Princeton, New Jersey ; Chichester, England : Princeton University Press, 2000.

Language Note:

English

Summary:

One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980's in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.

Contents:

Front matter

Contents

Acknowledgments / Rubin, Karl

Introduction

Chapter 1. Galois Cohomology of p-adic Representations

Chapter 2. Euler Systems: Definition and Main Results

Chapter 3. Examples and Applications

Chapter 4. Derived Cohomology Classes

Chapter 5. Bounding the Selmer Group

Chapter 6. Twisting

Chapter 7. Iwasawa Theory

Chapter 8. Euler Systems and p-adic L-functions

Chapter 9. Variants

Appendix A. Linear Algebra

Appendix B. Continuous Cohomology and Inverse Limits

Appendix C. Cohomology of p-adic Analytic Groups

Appendix D. p-adic Calculations in Cyclotomic Fields

Bibliography

Index of Symbols

Subject Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-691-05075-9

1-4008-6520-4

OCLC:

887499496