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

Shotton, Jack

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
• Public URL: https://durham-repository.worktribe.com/output/1319416
• Related Public URLs: https://arxiv.org/abs/1309.1600