Skip to Main Content

Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Représentations localement analytiques de $\textbf {GL}_2(\mathbf {Q}_p)$ et $(\varphi ,\Gamma )$-modules
HTML articles powered by AMS MathViewer

by Pierre Colmez
Represent. Theory 20 (2016), 187-248
Published electronically: July 15, 2016


We extend the $p$-adic local Langlands correspondence for $\textbf {GL}_2(\mathbf {Q}_p)$ to a correspondence $\Delta \mapsto \Pi (\Delta )$ between $(\varphi ,\Gamma )$-modules of rank $2$ over the Robba ring and certain locally analytic representations of $\textbf {GL}_2(\mathbf {Q}_p)$. If $\Delta$ is isocline, one uses the existing correspondence; in the remaining cases one builds a $\textbf {GL}_2(\mathbf {Q}_p)$-module from parabolically induced locally analytic representations and their duals. This construction extends to $\textbf {GL}_2(F)$ if $F$ is a finite extension of $\mathbf {Q}_p$, which suggests that the same should be true for the correspondence $\Delta \mapsto \Pi (\Delta )$.

Résumé. Nous étendons la correspondance de Langlands locale $p$-adique pour $\textbf {GL}_2(\mathbf {Q}_p)$ en une correspondance $\Delta \mapsto \Pi (\Delta )$ entre les $(\varphi ,\Gamma )$-modules de rang 2 sur l’anneau de Robba et certaines représentations localement analytiques de $\textbf {GL}_2(\mathbf {Q}_p)$. Si $\Delta$ est isocline, on se ramène à la correspondance déjà établie ; dans le cas contraire, on construit un $\textbf {GL}_2(\mathbf {Q}_p)$-module formé d’induites paraboliques localement analytiques et de leurs duales. Cette construction s’étend à $\textbf {GL}_2(F)$, si $F$ est une extension finie de $\mathbf {Q}_p$, ce qui suggère qu’il en est de même de la correspondance $\Delta \mapsto \Pi (\Delta )$.

Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 22E50
  • Retrieve articles in all journals with MSC (2010): 22E50
Bibliographic Information
  • Pierre Colmez
  • Affiliation: Institut de mathématiques de Jussieu, Centre National de la Recherche Scientifique, 4 place Jussieu, 75005 Paris, France
  • MR Author ID: 50720
  • Email:
  • Received by editor(s): November 28, 2015
  • Received by editor(s) in revised form: June 10, 2016
  • Published electronically: July 15, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Represent. Theory 20 (2016), 187-248
  • MSC (2010): Primary 22E50
  • DOI:
  • MathSciNet review: 3522263