On some modular representations of the Borel subgroup of GL_2(Q_p)
Number Theory
2019-02-20 v5 Representation Theory
Abstract
Colmez has given a recipe to associate a smooth modular representation Omega(W) of the Borel subgroup of GL_2(Q_p) to a F_p^bar-representation W of Gal(Qp^bar/Qp) by using Fontaine's theory of (phi,Gamma)-modules. We compute Omega(W) explicitly and we prove that if W is irreducible and dim(W)=2, then Omega(W) is the restriction to the Borel subgroup of GL_2(Q_p) of the supersingular representation associated to W in Breuil's correspondence.
Keywords
Cite
@article{arxiv.0810.5083,
title = {On some modular representations of the Borel subgroup of GL_2(Q_p)},
author = {Laurent Berger},
journal= {arXiv preprint arXiv:0810.5083},
year = {2019}
}
Comments
version 5 : final version, to appear in "Compositio Mathematica"