Galois representations and torsion in the coherent cohomology of Hilbert modular varieties

Abstract

Abstract Let F be a totally real number field and let p be a prime unramified in F. We prove the existence of Galois pseudo-representations attached to mod ⁡ p m ${\operatorname{mod}p^{m}}$ Hecke eigenclasses of paritious weight occurring in the coherent cohomology of Hilbert modular varieties for F of level prime to p.