Local constancy for the reduction mod p of 2-dimensional crystalline representations
Number Theory
2014-02-26 v2
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 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.
Keywords
Cite
@article{arxiv.0907.0221,
title = {Local constancy for the reduction mod p of 2-dimensional crystalline representations},
author = {Laurent Berger},
journal= {arXiv preprint arXiv:0907.0221},
year = {2014}
}
Comments
The "local constancy" part is new; the algorithm is unchanged; the title of the article has been changed