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$p$-DIVISIBILITY FOR COHERENT COHOMOLOGY

Part of: Commutative algebra: Homological methods (Co)homology theory

Published online by Cambridge University Press:  13 August 2015

BHARGAV BHATT
BHARGAV BHATT*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA; bhargav.bhatt@gmail.com

Abstract

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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.

MSC classification

Primary: 14F17: Vanishing theorems
Secondary: 14F30: $p$-adic cohomology, crystalline cohomology 13D22: Homological conjectures (intersection theorems)
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 3 , 2015 , e15
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author 2015

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