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 Cassels-Tate 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 pro-finite groups
• Duality theorems for Galois cohomology revisited
• Selmer complexes
• Unramified cohomology
• Iwasawa theory
• Classical Iwasawa theory
• Generalized Cassels-Tate pairings
• $R$-valued height pairings
• Parity of ranks of Selmer groups
• Errata
• List of symbols
• Bibliography