Absolute integral closure in positive characteristic
Commutative Algebra
2016-09-07 v1 Algebraic Geometry
Abstract
Let R be a local Noetherian domain of positive characteristic. A theorem of Hochster and Huneke (1992) states that if R is excellent, then the absolute integral closure of R is a big Cohen-Macaulay algebra. We prove that if R is the homomorphic image of a Gorenstein local ring, then all the local cohomology (below the dimension) of such a ring maps to zero in a finite extension of the ring. There results an extension of the original result of Hochster and Huneke to the case in which R is a homomorphic image of a Gorenstein local ring, and a considerably simpler proof of this result in the cases where the assumptions overlap, e.g., for complete Noetherian local domains.
Cite
@article{arxiv.math/0604046,
title = {Absolute integral closure in positive characteristic},
author = {Craig Huneke and Gennady Lyubeznik},
journal= {arXiv preprint arXiv:math/0604046},
year = {2016}
}