| eBook ISBN: | 978-1-4704-2448-0 |
| Product Code: | CBMS/88.E |
| List Price: | $40.00 |
| Individual Price: | $32.00 |
| eBook ISBN: | 978-1-4704-2448-0 |
| Product Code: | CBMS/88.E |
| List Price: | $40.00 |
| Individual Price: | $32.00 |
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Book DetailsCBMS Regional Conference Series in MathematicsVolume: 88; 1996; 137 ppMSC: Primary 13; Secondary 14
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.
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.
- Numerous exercises with solutions.
ReadershipGraduate students and research mathematicians interested in commutative rings and algebras.
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Table of Contents
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Chapters
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1. Introduction
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2. A prehistory of tight closure (Chapter 0)
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3. Basic Notions (Chapter 1)
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4. Test elements and the persistence of tight closure (Chapter 2)
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5. Colon-capturing and direct summands of regular rings (Chapter 3)
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6. F-Rational rings and rational singularities (Chapter 4)
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7. Integral closure and tight closure (Chapter 5)
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8. The Hilbert-Kunz multiplicity (Chapter 6)
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9. Big Cohen-Macaulay algebras (Chapter 7)
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10. Big Cohen-Macaulay algebras II (Chapter 8)
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11. Applications of big Cohen-Macaulay algebras (Chapter 9)
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12. Phantom homology (Chapter 10)
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13. Uniform Artin-Rees theorems (Chapter 11)
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14. The localization problem (Chapter 12)
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15. Regular base change (Chapter 13)
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16. The notion of tight closure in equal characteristic zero (Appendix 1)
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17. Solutions to exercises (Appendix 2)
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Reviews
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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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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Reviews
- Requests
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.
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.
- Numerous exercises with solutions.
Graduate students and research mathematicians interested in commutative rings and algebras.
-
Chapters
-
1. Introduction
-
2. A prehistory of tight closure (Chapter 0)
-
3. Basic Notions (Chapter 1)
-
4. Test elements and the persistence of tight closure (Chapter 2)
-
5. Colon-capturing and direct summands of regular rings (Chapter 3)
-
6. F-Rational rings and rational singularities (Chapter 4)
-
7. Integral closure and tight closure (Chapter 5)
-
8. The Hilbert-Kunz multiplicity (Chapter 6)
-
9. Big Cohen-Macaulay algebras (Chapter 7)
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10. Big Cohen-Macaulay algebras II (Chapter 8)
-
11. Applications of big Cohen-Macaulay algebras (Chapter 9)
-
12. Phantom homology (Chapter 10)
-
13. Uniform Artin-Rees theorems (Chapter 11)
-
14. The localization problem (Chapter 12)
-
15. Regular base change (Chapter 13)
-
16. The notion of tight closure in equal characteristic zero (Appendix 1)
-
17. Solutions to exercises (Appendix 2)
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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
