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Tight closure

Author: Winfried Bruns
Journal: Bull. Amer. Math. Soc. 33 (1996), 447-457
MSC (1991): Primary 13A35, 13A50, 13B21, 13D25, 13H10, 14B05
MathSciNet review: 1397097
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Abstract: The theory of tight closure was created by Mel Hochster and Craig Huneke about ten years ago. Assisted by numerous contributions of others, they have continuously developed the theory since then. `Tight closure' can now be regarded as a synonym for `characteristic $p$ methods in commutative algebra'. It ties several strands of commutative algebra and algebraic geometry together: invariant theory, rational singularities, the Briançon--Skoda theorem, the `homological conjectures', big Cohen--Macaulay modules and algebras, and various other topics.

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Additional Information

Winfried Bruns
Affiliation: Universität Osnabrück, FB Mathematik/Informatik, 49069 Osnabrück, Germany

Keywords: Tight closure, characteristic $p$ methods, invariant theory, rational singularities, Briançon--Skoda theorem, homological conjectures, phantom homology
Received by editor(s): March 21, 1996
Received by editor(s) in revised form: May 27, 1996
Article copyright: © Copyright 1996 American Mathematical Society

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