Tight closure and its applications / Craig Huneke

Auteur principal : Huneke, Craig, 1951-, AuteurCo-auteur collectivité : NSF-CBMS conference, 1995, AuteurType de document : MonographieCollection : Regional conference series in mathematics, 88Langue : anglais.Pays: Etats Unis.Éditeur : Providence (R.I.) : American Mathematical Society, cop. 1996Description : 1 vol. (IX-137 p.) ; 26 cmISBN: 082180412X.ISSN: 0160-7642.Bibliographie : Bibliogr. p. 133-137.Sujet MSC : 13A35, General commutative ring theory, Characteristic p methods and reduction to characteristic p; tight closure
13B22, Commutative ring extensions and related topics, Integral closure of commutative rings and ideals; integrally closed rings, related rings
13-02, Research exposition (monographs, survey articles) pertaining to commutative algebraEn-ligne : sommaire
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Expository lectures from the NSF-CBMS regional conference held at North Dakota State University, Fargo, ND, June 22-29, 1995

Bibliogr. p. 133-137

Tight closure is a method to study rings of equicharacteristic by using reduction to positive characteristic. In this book, the basic properties of tight closure are covered, including various types of singularities, e.g. F-regular and F-rational singularities. Basic theorems in the theory are presented including versions of the Briançon-Skoda theorem, various homological conjectures, and the Hochster-Roberts/Boutot theorems on invariants of reductive groups.

Several applications of the theory are given. These include the existence of big Cohen-Macaulay algebras and various uniform Artin-Rees theorems. (Source : AMS)

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