-DIVISIBILITY FOR COHERENT COHOMOLOGY

Abstract

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.