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ANR funded project

Tremplin-ERC (T-ERC) 2016
Projet ProBaRe

p-adic Langlands Programme and p-adic Banach Representations

This project aims to investigate the p-adic Langlands Program, where p is a prime number. The ultimate goal of this program is to establish a correspondence between certain p-adic Banach space representations of some p-adic reductive groups and certain p-adic representations of the absolute Galois group of a p-adic local field. It is consequently linked to p-adic Hodge theory. Especially, this correspondence should describe integral p-adic properties of automorphic forms and Galois representations as for example p-adic interpolation. It began under the impulsion of Christophe Breuil and the case of the group of 2 by 2 invertible matrices in p-adic numbers was completely elucidated between years 2000 and 2010. It was a great achievement since it permitted to prove important conjectures on 2-dimensional Galois representations as the Fontaine-Mazur and Breuil-M\'ezard conjectures. The extension of this program to other groups is consequently a big challenge in Number Theory and the key toward a full understanding of p-adic properties of Galois representations and automorphic forms. However, this extension encounters very numerous difficulties : even the formulation of the expected correspondence is not clear. This project has for purpose to investigate this generalization with a focus on the methods of representation theory. The main objectifve of this project is to understand the structure and properties of locally analytic representations associated to p-adic Banach space representations going beyond the case of finite slope representations. A very important tool in this study is the action of the Harish-Chandra center on these representations together with their canonical dimension.

Partners

CNRS Centre National de la Recherche Scientifique (CNRS) - Délégation Régionale Ile-de-France Sud

ANR grant: 87 035 euros
Beginning and duration: janvier 2017 - 18 mois

 

ANR Programme: Tremplin-ERC (T-ERC) 2016

Project ID: ANR-16-TERC-0005

Project coordinator:
Monsieur Benjamin Schraen (Centre National de la Recherche Scientifique (CNRS) - Délégation Régionale Ile-de-France Sud)

 

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The project coordinator is the author of this abstract and is therefore responsible for the content of the summary. The ANR disclaims all responsibility in connection with its content.