Local deformation rings and a Breuil-M\'{e}zard conjecture when l\neq p
Number Theory
2020-07-28 v3
Abstract
We compute the deformation rings of two dimensional mod l representations of Gal(Fbar/F) with fixed inertial type, for l an odd prime, p a prime distinct from p and F/Q_p a finite extension. We show that in this setting (when p is also odd) an analogue of the Breuil-M\'{e}zard conjecture holds, relating the special fibres of these deformation rings to the mod l reduction of certain irreducible representations of GL_2(O_F).
Keywords
Cite
@article{arxiv.1309.1600,
title = {Local deformation rings and a Breuil-M\'{e}zard conjecture when l\neq p},
author = {Jack Shotton},
journal= {arXiv preprint arXiv:1309.1600},
year = {2020}
}
Comments
35 pages. Proof of Proposition 2.7 in published version is incorrect, but the proposition is correct. An erratum is included here