Hanneke Wiersema

On Galois representations associated to mod p partial weight one Hilbert modular forms

We study two-dimensional mod p representations of the absolute Galois group of totally real fields. Under some technical assumptions, we prove that such a representation is modular with respect to a partial weight one mod p Hilbert modular form if and only if each of its local representations above p has a crystalline lift with prescribed irregular Hodge--Tate weights. Our method consists of translating results from regular to irregular weights and vice versa. This partially resolves the partial weight one case of a geometric Serre weight conjecture by Diamond and Sasaki.