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.