Astérisque 2006; 559 pp; softcover Number: 310 ISBN10: 2856292275 ISBN13: 9782856292273 List Price: US$124 Individual Members: US$111.60 Order Code: AST/310
 This book builds new foundations of Iwasawa theory, based on a systematic study of cohomological invariants of big Galois representations in the framework of derived categories. A new duality formalism is developed, which leads to generalized CasselsTate pairings and generalized \(p\)adic height pairings. One of the applications is a parity result for Selmer groups associated to Hilbert modular forms. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in Iwasawa theory. Table of Contents  Introduction
 Homological algebra: Products and signs
 Local duality
 Continuous cohomology
 Continuous cohomology of profinite groups
 Duality theorems for Galois cohomology revisited
 Selmer complexes
 Unramified cohomology
 Iwasawa theory
 Classical Iwasawa theory
 Generalized CasselsTate pairings
 \(R\)valued height pairings
 Parity of ranks of Selmer groups
 Errata
 List of symbols
 Bibliography
