%0 Journal Article
%T On some modular representations of the Borel subgroup of GL_2(Q_p)
%A Laurent Berger
%J Mathematics
%D 2008
%I arXiv
%R 10.1112/S0010437X09004345
%X 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.
%U http://arxiv.org/abs/0810.5083v5