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CBMS Regional Conference Series in Mathematics
1996; 137 pp; softcover
List Price: US$38
Member Price: US$30.40
All Individuals: US$30.40
Order Code: CBMS/88
This monograph 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 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.
Graduate students and research mathematicians interested in commutative rings and algebras.
"The book [is] easily readable by a person who wants to study tight closure in depth as well as by a person who wants to read lightly and still gain some understanding."
-- Zentralblatt MATH
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