vix.ing · top · new · best · stats · spec

Annihilating the cohomology of group schemes

2011/09/12 by Bhargav Bhatt, Bhatt, Bhargav
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1109.2383

openalex publication_date 2011/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Related