%0 Journal Article
%T Un calcul d'anneaux de d¨¦formations potentiellement Barsotti--Tate
%A Xavier Caruso
%A Agn¨¨s David
%A Ariane M¨¦zard
%J Mathematics
%D 2014
%I arXiv
%X Let F be an unramified extension of Qp. The first aim of this work is to develop a purely local method to compute the potentially Barsotti-Tate deformations rings with tame Galois type of irreducible two-dimensional representations of the absolute Galois group of F. We then apply our method in the particular case where F has degree 2 over Q_p and determine this way almost all these deformations rings. In this particular case, we observe a close relationship between the structure of these deformations rings and the geometry of the associated Kisin variety. As a corollary and still assuming that F has degree 2 over Q_p, we prove, except in two very particular cases, a conjecture of Kisin which predicts that intrinsic Galois multiplicities are all equal to 0 or 1.
%U http://arxiv.org/abs/1402.2616v1