Local deformation rings for GL2 and a Breuil–Mézard conjecture when l≠p

Shotton, Jack

doi:10.2140/ant.2016.10.1437

Local deformation rings for GL2 and a Breuil–Mézard conjecture when l≠p

Shotton, Jack

Authors

Dr Jack Shotton jack.g.shotton@durham.ac.uk
Assistant Professor

Abstract

We compute the deformation rings of two dimensional mod l rep- resentations of Gal(F/F) with fixed inertial type, for l an odd prime, p a prime distinct from l, and F/Qp a finite extension. We show that in this set- ting an analogue of the Breuil–M´ezard conjecture holds, relating the special fibres of these deformation rings to the mod l reduction of certain irreducible representations of GL2(OF ).

Citation

Shotton, J. (2016). Local deformation rings for GL2 and a Breuil–Mézard conjecture when l≠p. Algebra & Number Theory, 10(7), 1437-1475. https://doi.org/10.2140/ant.2016.10.1437

Journal Article Type	Article
Acceptance Date	Jul 18, 2016
Online Publication Date	Sep 27, 2016
Publication Date	Sep 27, 2016
Deposit Date	Sep 20, 2018
Publicly Available Date	Nov 27, 2018
Journal	Algebra & Number Theory
Print ISSN	1937-0652
Electronic ISSN	1944-7833
Publisher	Mathematical Sciences Publishers (MSP)
Peer Reviewed	Peer Reviewed
Volume	10
Issue	7
Pages	1437-1475
DOI	https://doi.org/10.2140/ant.2016.10.1437
Related Public URLs	https://arxiv.org/abs/1309.1600

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Copyright Statement
First published in Algebra & Number Theory in Vol. 10 (2016), No. 7, 1437–1475, published by Mathematical Sciences Publishers. © 2016 Mathematical Sciences Publishers. All rights reserved.