**Astérisque**

Volume: 330;
2010;
554 pp;
Softcover

MSC: Primary 11;
**Print ISBN: 978-2-85629-281-5
Product Code: AST/330**

List Price: $105.00

AMS Member Price: $86.40

# Représentations \(p\)-adiques de Groupes \(p\)-adiques II: Représentations de \(\mathbf{GL}_{2}(\mathbf{Q}_{p})\) et \((𝜑,Γ)\)-Modules

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*Laurent Berger; Christophe Breuil; Pierre Colmez*

A publication of the Société Mathématique de France

This second volume is devoted to applications of Fontaine's theory of \((\varphi,\Gamma)\)-modules to that of \(p\)-adic unitary representations of \({\mathbf GL}_2({\mathbf Q}_p)\), whose aim is to construct a (\(p\)-adic local Langlands) correspondence between these representations and \(2\)-dimensional \(p\)-adic representations of the absolute Galois group of \({\mathbf Q}_p\). In this volume the reader will find an overview of classical \(p\)-adic functional analysis, diverse features of the unitary principal series of \({\mathbf GL}_2({\mathbf Q}_p)\), and the construction of functors building bridges between the world of Galois representations and that of representations of \({\mathbf GL}_2({\mathbf Q}_p)\) and its mirabolic subgroup.

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 number theory.