%0 Journal Article
%T Local constancy for the reduction mod p of 2-dimensional crystalline representations
%A Laurent Berger
%J Mathematics
%D 2009
%I arXiv
%R 10.1112/blms/bdr105
%X Irreducible crystalline representations of dimension 2 of Gal(Qpbar/Qp) depend up to twist on two parameters, the weight k and the trace of frobenius a_p. We show that the reduction modulo p of such a representation is a locally constant function of a_p (with an explicit radius) and a locally constant function of the weight k if a_p <> 0. We then give an algorithm for computing the reductions modulo p of these representations. The main ingredient is Fontaine's theory of (phi,Gamma)-modules as well as the theory of Wach modules.
%U http://arxiv.org/abs/0907.0221v2