  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.
