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- DescriptionThis mograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995. 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 Briancon-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.It features: the existence of test elements; a study of F-rational rings and rational singularities; basic information concerning the Hilbert-Kunz function, phantom homology, and regular base change for tight closure; and, numerous exercises with solutions.
- Author(s)Craig Huneke
- PublisherAmerican Mathematical Society
- Date of Publication15/03/1996
- Series TitleCBMS Regional Conference Series in Mathematics
- Series Part/Volume NumberNo. 88
- Place of PublicationProvidence
- Country of PublicationUnited States
- ImprintAmerican Mathematical Society
- Weight255 g
- Height230 mm
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