Let R be a local Noetherian domain of positive characteristic. A theorem of Hochster and Huneke [M. Hochster, C. Huneke, Infinite integral extensions and big Cohen-Macaulay algebras, Ann. of Math. 135 (1992) 53-89] 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. As a result there follow 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.
Bibliographical noteFunding Information:
✩ NSF support for both authors is gratefully acknowledged. The first author was supported in part by grant DMS-0244405, and the second by grant DMS-0202176. * Corresponding author. E-mail addresses: email@example.com (C. Huneke), firstname.lastname@example.org (G. Lyubeznik).
- Absolute integral closure
- Characteristic p
- Local cohomology
- Tight closure