Sur quelques repr\'esentations potentiellement cristallines de GL_2(Q_p)
Number Theory
2010-02-22 v1 Representation Theory
Abstract
To each 2-dimensional irreducible p-adic representation of Gal(Qpbar/Qp) which becomes crystalline over an abelian extension of Q_p, we associate a Banach space B(V) endowed with a linear continuous unitary action of GL_2(Q_p). When V is moreover phi-semi-simple, we use the (phi,Gamma)-module and the Wach module associated to V to show that the representation B(V) is nonzero, topologically irreducible and admissible.
Keywords
Cite
@article{arxiv.math/0601545,
title = {Sur quelques repr\'esentations potentiellement cristallines de GL_2(Q_p)},
author = {L. Berger and C. Breuil},
journal= {arXiv preprint arXiv:math/0601545},
year = {2010}
}