Algebra & Number Theory

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

Jack Shotton

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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).

Article information

Source
Algebra Number Theory, Volume 10, Number 7 (2016), 1437-1475.

Dates
Received: 28 April 2015
Revised: 14 April 2016
Accepted: 18 July 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842566

Digital Object Identifier
doi:10.2140/ant.2016.10.1437

Mathematical Reviews number (MathSciNet)
MR3554238

Zentralblatt MATH identifier
06633202

Subjects
Primary: 11S37: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]

Keywords
Galois representations deformation rings local Langlands Breuil–Mézard

Citation

Shotton, Jack. Local deformation rings for $\operatorname{GL}_2$ and a Breuil–Mézard conjecture when $l \neq p$. Algebra Number Theory 10 (2016), no. 7, 1437--1475. doi:10.2140/ant.2016.10.1437. https://projecteuclid.org/euclid.ant/1510842566


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