On flagged framed deformation problems of local crystalline Galois representations

JOURNAL OF NUMBER THEORY

卷:199

Article

Kalloniatis, Tristan¹ 

[1] Kings Coll London, London WC2R 2LS, England

关键词: Crystalline Galois cohomology;    Deformation theory;    Galois representations;   

DOI  :  10.1016/j.jnt.2018.11.010

来源: Elsevier

【 摘 要 】

We prove that irreducible residual crystalline representations of the absolute Galois group of an unramified extension of Q(p) have smooth representable crystalline framed deformation problems, provided that the Hodge-Tate weights lie in the Fontaine-Laffaille range. We then extend this result to the flagged lifting problem associated to any Fontaine-Laffaille upper triangular representation whose flag is of maximal length. We calculate the relative dimension of these various crystalline lifting functors in terms of the underlying Hodge Tate weight structures, and also apply these results to give an alternative proof of the fact that every such residual representation admits a so-called universally twistable lift. Finally we give some brief indications as to the various directions in which these results might be generalised. Crown Copyright (C) 2018 Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free