Absolute integral closure in positive characteristic

Craig Huneke, Gennady Lyubeznik

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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
Issue number2
StatePublished - Apr 1 2007


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


Dive into the research topics of 'Absolute integral closure in positive characteristic'. Together they form a unique fingerprint.

Cite this