Absolute integral closure in positive characteristic |
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Authors: | Craig Huneke Gennady Lyubeznik |
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Institution: | aDepartment of Mathematics, University of Kansas, Lawrence, KS 66045, USA;bDepartment of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA |
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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. |
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Keywords: | Absolute integral closure Local cohomology Tight closure Characteristic p Cohen– Macaulay |
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