arXiv:1204.5831 p-divisibility for coherent cohomology from arXiv Front: math.NT by Bhargav Bhatt We prove that the coherent cohomology of a proper morphism of noetherian schemes can be made arbitrarily p-divisible by passage to proper covers (for a fixed prime p). Under some extra conditions, we also show that p-torsion can be killed by passage to proper covers. These results are motivated by the desire to understand rational singularities in mixed characteristic, and have applications in p-adic Hodge theory
nLab page on Coherent cohomology