Let F be a totally real number field, p a prime number, and M the (splitting model of) Hilbert modular variety for F (of some fixed level) defined over a finite field of characteristic p. I will explain how exploiting the geometry of M, and in particular the existence of the partial Hasse invariants, one can attach Galois representations to Hecke eigensystems occurring in the coherent cohomology of M. This is a joint work with Matthew Emerton and Davide Reduzzi.