Modularity in the partial weight one case

Hanneke Wiersema (University of Cambridge)

07-Dec-2022, 16:00-17:00 (16 months ago)

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–-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. Time permitting, we will also discuss a $p$-adic Hodge theoretic version of this.

number theory

Audience: researchers in the topic


London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html

Organizers: Caleb Springer*, Luis Garcia*
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