Workshop on Motives, Galois Representations and Cohomology around the Langlands Program

Models for Galois deformation rings

Abstract: An important input into modularity lifting theorems is an understanding of the geometry of Galois deformation rings, especially local deformation rings with p-adic Hodge theory conditions at $\ell=p$. Outside of a few cases (ordinary, Fontaine-Laffaille...), the detailed structure of these deformation rings is very mysterious. I will introduce models which in generic situations conjecturally have the same singularities as those of a class of potentially crystalline deformation rings. This will ultimately have applications to the weight part of Serre's conjecture, the Breuil-Mèzard conjecture, and modularity lifting in dimension $> 3$ where relatively little is known. This is joint work with Daniel Le, Bao V. Le Hung, and Stefano Morra.

Date & Time

November 09, 2017 | 4:00pm – 5:00pm

Location

S-101

Speakers

Brandon Levin

Affiliation

University of Chicago

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