Vol. 10, No. 7, 2016

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

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

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
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
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
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