Number Theory Seminar

Daniel LeUniversity of Toronto
The weight part of Serre's conjecture

Friday, March 16, 2018 - 2:30pm
Malott 206

In the 70's, Serre conjectured that all odd irreducible mod p Galois representations arise from modular forms. A decade later, he conjectured a recipe for the weight and level of the modular forms in terms of the Galois representations--a recipe which would play a key role in the proof of Fermat's Last Theorem. In Serre's original context, these conjectures are now known. We survey recent conjectures and results about the weight part of Serre's conjecture for more general automorphic forms. The main ingredient is a description of local Galois deformation rings using local models. This is joint work with B.V. Le Hung, B. Levin, and S. Morra.