p-divisibility for coherent cohomology

TL;DR

This paper demonstrates that the coherent cohomology of proper morphisms can be made arbitrarily divisible by a prime p through proper covers, aiding the study of rational singularities in mixed characteristic and p-adic Hodge theory.

Contribution

It establishes p-divisibility and p-torsion elimination in coherent cohomology via proper covers, advancing understanding in mixed characteristic geometry.

Findings

Coherent cohomology can be made arbitrarily p-divisible via proper covers.

Under certain conditions, p-torsion can be eliminated by proper covers.

Results have applications in p-adic Hodge theory and rational singularities.

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