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.

Table of Contents

• M.-F. Vigneras -- Banach \(\ell\)-adic representations of \(p\)-adic groups
• P. Colmez -- Fonctions d'une variable \(p\)-adique
• P. Colmez -- \((\varphi, \Gamma)\)-modules et représentations du mirabolique de \(\mathbf{GL}_2(\mathbf{Q}_p)\)
• L. Berger and C. Breuil -- Sur quelques représentations potentiellement cristallines de \(\mathrm{GL}_2(\mathbf{Q}_p)\)
• P. Colmez -- La série principale unitaire de \(\mathbf{GL}_2(\mathbf{Q}_p)\)
• L. Berger -- Représentations modulaires de \(\mathrm{GL}_2(\mathbf{Q}_p)\) et représentations galoisiennes de dimension \(2\)
• P. Colmez -- Représentations de \(\mathbf{GL}_2(\mathbf{Q}_p)\) et \((\varphi, \Gamma)\)-modules
• M. Kisin -- Deformations of \(G_{\mathbb{Q}_p}\) and \(\mathrm{GL}_2(\mathbb{Q}_p)\) representations
• G. Böckle -- Deformation rings for some mod \(3\) Galois representations of the absolute Galois group of \(\mathbf{Q}_3\)
• F. Andreatta and A. Iovita -- Erratum to the article: Global applications to relative \((\varphi,\Gamma)\)-modules, I