Euler Systems. (AM-147)
Karl Rubin

Paper | 2000 | $55.00 / £37.95
240 pp. | 6 x 9

Shopping Cart | Table of Contents

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.

Table of Contents

Series:

• Annals of Mathematics Studies
  Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors

Subject Area:

• Mathematics

VISIT OUR MATH WEBSITE

Shopping Cart:

For customers in the U.S., Canada, Latin America, Asia, and Australia
Paper: $55.00 ISBN13: 978-0-691-05076-8

For customers in Europe, Africa, the Middle East, and India
Paper: £37.95 ISBN13: 978-0-691-05076-8

Prices subject to change without notice

File created: 6/4/2009

Questions and comments to: webmaster@press.princeton.edu
Princeton University Press