$p$-DIVISIBILITY FOR COHERENT COHOMOLOGY. (1st August 2015) - BHATT, BHARGAV
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.