Tight Closure and Its Applications
Seiten
1996
American Mathematical Society (Verlag)
978-0-8218-0412-4 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-0412-4 (ISBN)
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Deals with the theory of tight closure and its applications. This book covers the basic properties of tight closure including various types of singularities such as F-regular and F-rational singularities. It presents basic theorems in the theory including versions of the Briancon-Skoda theorem, and various homological conjectures.
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 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.
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 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.
Acknowledgements Introduction Relationship chart A prehistory of tight closure Basic notions Test elements and the persistence of tight closure Colon-capturing and direct summands of regular rings F-rational rings and rational singularities Integral closure and tight closure The Hilbert-Kunz multiplicity Big Cohen-Macaulay algebras Big Cohen-Macaulay algebras II Applications of big Cohen-Macaulay algebras Phantom homology Uniform Artin-Rees theorems The localization problem Regular base change Appendix 1: The notion of tight closure in equal characteristic zero (by M. Hochster) Appendix 2: Solutions to the exercises Bibliography.
| Erscheint lt. Verlag | 1.6.1996 |
|---|---|
| Reihe/Serie | CBMS Regional Conference Series in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 290 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8218-0412-X / 082180412X |
| ISBN-13 | 978-0-8218-0412-4 / 9780821804124 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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