Euler Systems. (AM-147), Volume 147

Karl Rubin

Published by Princeton University Press 2000

Euler Systems. (AM-147), Volume 147

Karl Rubin

Volume 147 in the series Annals of Mathematics Studies

https://doi.org/10.1515/9781400865208

Overview
Contents

About this book

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 1980s 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.

Author / Editor information

Karl Rubin, Professor of Mathematics at Stanford University, was awarded the Cole Prize of the American Mathematical Society in 1992. He has been a Guggenheim Fellow, a Sloan Fellow, and a National Science Foundation Presidential Young Investigator.

Topics

Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	vii
Acknowledgments Karl Rubin Requires Authentication Unlicensed Licensed Download PDF	xi
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 1. Galois Cohomology of p-adic Representations Requires Authentication Unlicensed Licensed Download PDF	9
Chapter 2. Euler Systems: Definition and Main Results Requires Authentication Unlicensed Licensed Download PDF	33
Chapter 3. Examples and Applications Requires Authentication Unlicensed Licensed Download PDF	47
Chapter 4. Derived Cohomology Classes Requires Authentication Unlicensed Licensed Download PDF	75
Chapter 5. Bounding the Selmer Group Requires Authentication Unlicensed Licensed Download PDF	105
Chapter 6. Twisting Requires Authentication Unlicensed Licensed Download PDF	119
Chapter 7. Iwasawa Theory Requires Authentication Unlicensed Licensed Download PDF	129
Chapter 8. Euler Systems and p-adic L-functions Requires Authentication Unlicensed Licensed Download PDF	163
Chapter 9. Variants Requires Authentication Unlicensed Licensed Download PDF	175
Appendix A. Linear Algebra Requires Authentication Unlicensed Licensed Download PDF	189
Appendix B. Continuous Cohomology and Inverse Limits Requires Authentication Unlicensed Licensed Download PDF	195
Appendix C. Cohomology of p-adic Analytic Groups Requires Authentication Unlicensed Licensed Download PDF	205
Appendix D. p-adic Calculations in Cyclotomic Fields Requires Authentication Unlicensed Licensed Download PDF	211
Bibliography Requires Authentication Unlicensed Licensed Download PDF	219
Index of Symbols Requires Authentication Unlicensed Licensed Download PDF	223
Subject Index Requires Authentication Unlicensed Licensed Download PDF	227