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

• Record Type: Journal Article
• Authors: BHATT, BHARGAV
• Is Part Of: Forum of mathematics. Volume 3(2015)
• Publication Date: 2015-08-01
• Subjects: 14F17 (primary), -- 14F30, -- 13D22 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2015.11
• Languages: English
• ISSNs: 2050-5094

Abstract

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.