Annihilating the cohomology of group schemes

Bhatt, Bhargav

doi:10.2140/ant.2012.6.1561

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Annihilating the cohomology of group schemes

Bhargav Bhatt

Vol. 6 (2012), No. 7, 1561–1577

DOI: 10.2140/ant.2012.6.1561

Abstract

Our goal in this note is to show that cohomology classes with coefficients in finite flat group schemes can be killed by finite covers of the base scheme, and similarly for abelian schemes with “finite covers” replaced by “proper covers.” We apply this result to commutative algebra to give by a conceptual proof of Hochster–Huneke’s theorem on the existence of big Cohen–Macaulay algebras in positive characteristic; all previous proofs of this result were equational or cocycle-theoretic in nature.

Keywords

group schemes, abelian varieties, étale cohomology, fppf cohomology, big Cohen–Macaulay algebras

Mathematical Subject Classification 2010

Primary: 14L15

Secondary: 13D45, 14K05, 14F20

Milestones

Received: 26 September 2011

Revised: 6 December 2011

Accepted: 3 January 2012

Published: 4 December 2012

Authors

Bhargav Bhatt
Department of Mathematics University of Michigan 2074 East Hall 530 Church Street Ann Arbor, MI 48109 United States	School of Mathematics Institute for Advanced Study Princeton, NJ 08540 United States
http://www-personal.umich.edu/~bhattb/

Vol. 6, No. 7, 2012