Local constancy for the reduction mod p of 2-dimensional crystalline representations
Abstract
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 ap. We show that the reduction modulo p of such a representation is a locally constant function of ap (with an explicit radius) and a locally constant function of the weight k if ap <> 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.
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