Arithmetic Geometry and Number Theory RTG Seminar: The Breuil-Mezard conjecture for potentially crystalline deformation rings

Seminar | February 25 | 3-5 p.m. | 748 Evans Hall

 Brandon Levin, University of Arizona

 Department of Mathematics

The Breuil-Mezard conjecture predicts the geometry of local Galois deformation rings with p-adic Hodge theory condition in terms of modular representation theory. I will begin by reformulating this conjecture in terms of the Emerton-Gee moduli stack of mod p Galois representations. I will then describe joint work in progress with Daniel Le, Bao V. Le Hung, and Stefano Morra where we prove the conjecture in generic situations for a class of potentially crystalline deformation rings. The key ingredient is the construction of a local model which models the singularities of these Galois deformation rings.