Annihilating the cohomology of group schemes

Details Annihilating the cohomology of group schemes Annihilating the cohomology of group schemes

2011-09-12

arxiv.org/abs/1109.2383v1

Mathematics

Algebraic Geometry

12 pages, comments welcome!

Scientific paper

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 by giving a new and more 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.

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