Représentations P-Adiques de Groupes P-Adiques

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...
More Description

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.