**Astérisque**

Volume: 324;
2009;
314 pp;
Softcover

MSC: Primary 11; 14; 20;
Secondary 15

**Print ISBN: 978-2-85629-264-8
Product Code: AST/324**

List Price: $105.00

Individual Member Price: $86.40

# Families of Galois Representations and Selmer Groups

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*Joël Bellaïche; Gaëtan Chenevier*

A publication of the Société Mathématique de France

This book presents an in-depth study of the families of
Galois representations carried by the \(p\)-adic eigenvarieties
attached to unitary groups. The study encompasses some general
algebraic aspects (properties of the space of representations of a
group in the neighborhood of a point, reducibility loci,
pseudocharacters), and other aspects more specific to Galois groups of
local or number fields. In particular, the authors define and study certain
deformation functors of crystalline representations of the absolute
Galois group of \(\mathbb{Q}p\), namely *trianguline
deformations*, which are naturally associated to the families
above.

As an application, the authors show how the geometry of these eigenvarieties at “classical” points is related to the dimension of certain Selmer groups. This, combined with conjectures of Langlands and Arthur on the discrete automorphic spectrum of unitary groups, allows the authors to prove, among other things, new cases of the Bloch–Kato conjectures (in any dimension).

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.

#### Table of Contents

# Table of Contents

## Families of Galois Representations and Selmer Groups

#### Readership

Graduate students and research mathematicians interested in number theory.