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

Matthew Emerton, Davide A. Reduzzi, Liang Xiao

Published 2013-07-30, updated 2014-07-10Version 2

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 $p^m$ Hecke eigenclasses of paritious weight occurring in the coherent cohomology of Hilbert modular varieties for $F$ of level prime to $p$.