Absolute integral closure in positive characteristic

By Craig Huneke, Gennady Lyubeznik. 2006

63 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/70626d45562a44fef88c27b4f2c7cd6843792099

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In Algebra and Number Theory

1. Irena Swanson
2. Craig Huneke
3. Juan Migliore
4. Brian Harbourne
5. R. Mir'o-Roig

In Geometry and Topology

1. Irena Swanson
2. Craig Huneke
3. Juan Migliore
4. Brian Harbourne
5. R. Mir'o-Roig

Citations in the corpus

• Integral closure of ideals, rings, and modules (2006, background): “In this section we give a proof, due to Huneke and Lyubeznik [142], of a fundamental result due to Hochster and Huneke [127] that says that the absolute integral closure of a complete local domain in characteristic p is Cohen–Macaulay.”