Absolute integral closure in positive characteristic

Craig Huneke, Gennady Lyubeznik

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22 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)498-504
Number of pages7
JournalAdvances in Mathematics
Volume210
Issue number2
DOIs
StatePublished - Apr 1 2007

Bibliographical note

Funding 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: huneke@math.ku.edu (C. Huneke), gennady@math.umn.edu (G. Lyubeznik).

Keywords

  • Absolute integral closure
  • Characteristic p
  • Cohen-Macaulay
  • Local cohomology
  • Tight closure

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