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 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.
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Contributor : Laurent Berger <>
Submitted on : Friday, July 1, 2011 - 1:45:01 PM
Last modification on : Thursday, January 11, 2018 - 6:12:31 AM

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  • HAL Id : hal-00605404, version 1
  • ARXIV : 0907.0221

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Laurent Berger. Local constancy for the reduction mod p of 2-dimensional crystalline representations. Bulletin of the London Mathematical Society, London Mathematical Society, 2012, 44 (3), pp.451--459. ⟨hal-00605404⟩

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