Vol. 10, No. 7, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12, 1 issue

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
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

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).

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