Vol. 10, No. 7, 2016

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Local deformation rings for $\operatorname{GL}_2$ and a Breuil–Mézard conjecture when $l \neq p$

Jack Shotton

Vol. 10 (2016), No. 7, 1437–1475
Abstract

We compute the deformation rings of two dimensional mod l representations of Gal(F¯F) with fixed inertial type for l an odd prime, p a prime distinct from l, and Fp a finite extension. We show that in this setting an analogue of the Breuil–Mézard conjecture holds, relating the special fibres of these deformation rings to the mod l reduction of certain irreducible representations of GL2(OF).

Keywords
Galois representations, deformation rings, local Langlands, Breuil–Mézard
Mathematical Subject Classification 2010
Primary: 11S37
Milestones
Received: 28 April 2015
Revised: 14 April 2016
Accepted: 18 July 2016
Published: 27 September 2016
Authors
Jack Shotton
University of Chicago
5442 S Ellis Ave
Chicago, IL 60615
United States