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Serre weight conjectures for unitary groups

Banff International Research Station for Mathematical Innovation and Discovery

In the 1970s, Serre formulated his remarkable conjecture that every two-dimensional mod-p Galois representation of the absolute Galois group of $\mathbb{Q}$, which is odd and irreducible, should come from a modular form. He later refined his conjecture, giving a precise recipe for the weight and level of the modular form. Both the "weak form" and "strong form" of Serreâs conjecture are now theorems, due to the work of many mathematicians (Khare-Wintenberger, Kisin, Edixhoven, Ribet, and others). In this talk, we will discuss how to generalize Serreâs weight recipe when the Galois representation is replaced by a homomorphism from an absolute Galois group to the Langlands dual of a rank 2 unitary group. This is joint work with Stefano Morra.

Mathematics; Number theory; Combinatorics; Arithmetic number theory

video/mp4

Author affiliation: University of Alberta

2019-11-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72226

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/