Modularity in the partial weight one case

Abstract: The strong form of Serre's conjecture states that a two-dimensional mod p representation of the absolute Galois group of $\mathbb{Q}$ arises from a modular form of a specific weight, level and character. Serre restricted to modular forms of weight at least 2, but Edixhoven later refined this conjecture to include weight one modular forms. In this talk we explore analogues of Edixhoven's refinement for Galois representations of totally real fields, extending recent work of Diamond and Sasaki. In particular, we show how modularity of partial weight one Hilbert modular forms can be related to modularity of Hilbert modular forms with regular weights, and vice versa. We will also discuss the applications of this for p-adic Hodge theory.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.