p-adic Hodge-theoretic properties of \'etale cohomology with mod p   coefficients, and the cohomology of Shimura varieties
  We show that the mod p cohomology of a smooth projective variety with semistable reduction over K, a finite extension of Qp, embeds into the reduction modulo p of a semistable Galois representation with Hodge-Tate weights in the expected range (at least after semisimplifying, in the case of the cohomological degree > 1). We prove refinements with descent data, and we apply these results to the cohomology of unitary Shimura varieties, deducing vanishing results and applications to the weight part of Serre's conjecture. 
Matthew Emerton and Toby Gee
math.NT