| eBook ISBN: | 978-1-4704-0067-5 |
| Product Code: | MEMO/103/490.E |
| List Price: | $36.00 |
| MAA Member Price: | $32.40 |
| AMS Member Price: | $21.60 |
| eBook ISBN: | 978-1-4704-0067-5 |
| Product Code: | MEMO/103/490.E |
| List Price: | $36.00 |
| MAA Member Price: | $32.40 |
| AMS Member Price: | $21.60 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 103; 1993; 91 ppMSC: Primary 13
This book uses a powerful new technique, tight closure, to provide insight into many different problems that were previously not recognized as related. The authors develop the notion of weakly Cohen-Macaulay rings or modules and prove some very general acyclicity theorems. These theorems are applied to the new theory of phantom homology, which uses tight closure techniques to show that certain elements in the homology of complexes must vanish when mapped to well-behaved rings. These ideas are used to strengthen various local homological conjectures. Initially, the authors develop the theory in positive characteristic, but it can be extended to characteristic 0 by the method of reduction to characteristic \(p\). The book would be suitable for use in an advanced graduate course in commutative algebra.
ReadershipAlgebraists and algebraic geometers interested in a deeper understanding of commutative algebra.
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Table of Contents
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Chapters
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1. Introduction
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2. Minheight and the weak Cohen-Macaulay property
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3. Acyclicity criteria with denominators for complexes of modules
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4. Vanishing theorems for maps of homology via phantom acyclicity
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5. Regular closure
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6. Intersection theorems via phantom acyclicity
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This book uses a powerful new technique, tight closure, to provide insight into many different problems that were previously not recognized as related. The authors develop the notion of weakly Cohen-Macaulay rings or modules and prove some very general acyclicity theorems. These theorems are applied to the new theory of phantom homology, which uses tight closure techniques to show that certain elements in the homology of complexes must vanish when mapped to well-behaved rings. These ideas are used to strengthen various local homological conjectures. Initially, the authors develop the theory in positive characteristic, but it can be extended to characteristic 0 by the method of reduction to characteristic \(p\). The book would be suitable for use in an advanced graduate course in commutative algebra.
Algebraists and algebraic geometers interested in a deeper understanding of commutative algebra.
-
Chapters
-
1. Introduction
-
2. Minheight and the weak Cohen-Macaulay property
-
3. Acyclicity criteria with denominators for complexes of modules
-
4. Vanishing theorems for maps of homology via phantom acyclicity
-
5. Regular closure
-
6. Intersection theorems via phantom acyclicity
