Galois extensions, plus closure, and maps on local cohomology

Details Galois extensions, plus closure, and maps on local cohomology Galois extensions, plus closure, and maps on local cohomology

2011-04-03

arxiv.org/abs/1104.0413v1

Advances in Mathematics 229 (2012) 1847-1861

Mathematics

Commutative Algebra

Scientific paper

Given a local domain $(R,m)$ of prime characteristic that is a homomorphic image of a Gorenstein ring, Huneke and Lyubeznik proved that there exists a module-finite extension domain $S$ such that the induced map on local cohomology modules $H^i_m(R)\to H^i_m(S)$ is zero for each $i<\dim R$. We prove that the extension $S$ may be chosen to be generically Galois, and analyze the Galois groups that arise.

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