Local deformation rings and a Breuil-Mézard conjecture when l\neq p

Abstract

We compute the deformation rings of two dimensional mod l representations of Gal(Fbar/F) with fixed inertial type, for l an odd prime, p a prime distinct from p and F/Q_p a finite extension. We show that in this setting (when p is also odd) 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 GL_2(O_F).

35 pages. Proof of Proposition 2.7 in published version is incorrect, but the proposition is correct. An erratum is included here

References in corpus (1)

• On the Breuil-Mézard conjecture

Cited by in corpus (6)

• The Breuil--Mézard conjecture when $l\ne p$
• Ihara's lemma for Shimura curves over totally real fields via patching
• On the modularity of 2-adic potentially semi-stable deformation rings
• Modularity lifting theorems
• Patching and Multiplicity $2^k$ for Shimura Curves
• On the constituents of the mod $p$ cohomology of Shimura curves