Vol. 14, No. 3, 2020

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On the locus of $2$-dimensional crystalline representations with a given reduction modulo $p$

Sandra Rozensztajn

Vol. 14 (2020), No. 3, 643–700
Abstract

We consider the family of irreducible crystalline representations of dimension 2 of Gal( ̄pp) given by the V k,ap for a fixed weight k 2. We study the locus of the parameter ap where these representations have a given reduction modulo p. We give qualitative results on this locus and show that for a fixed p and k it can be computed by determining the reduction modulo p of V k,ap for a finite number of values of the parameter ap. We also generalize these results to other Galois types.

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Keywords
Galois representations, p-adic representations
Mathematical Subject Classification 2010
Primary: 11F80
Secondary: 14G22
Milestones
Received: 13 September 2018
Revised: 26 August 2019
Accepted: 30 September 2019
Published: 1 June 2020
Authors
Sandra Rozensztajn
UMPA, ÉNS de Lyon
UMR 5669 du CNRS
Lyon
France