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Lecture notes on local rings Birger Iversen ; edited by Holger Andreas Nielsen.

By: Contributor(s): Material type: TextTextPublication details: New Jersey : World Scientific, 2014.Description: x, 213 p. ; 24 cmISBN:
  • 9789814603652 (hardcover : alk. paper)
Subject(s): DDC classification:
  • 512.4 23 Iv94
Contents:
1. Dimension of a local ring-- 2. Modules over a local ring-- 3.Divisor theory-- 4. Completion-- 5. Injective modules-- 6. Local cohomology-- 7. Dualizing complexes-- 8. Local duality-- 9. Amplitude and dimension-- 10. Intersection multiplicities-- 11. Complexes of free modules-- Bibliography-- Index.
Summary: "The content in Chapter 1-3 is a fairly standard one-semester course on local rings with the goal to reach the fact that a regular local ring is a unique factorization domain. The homological machinery is also supported by Cohen-Macaulay rings and depth. In Chapters 4-6 the methods of injective modules, Matlis duality and local cohomology are discussed. Chapters 7-9 are not so standard and introduce the reader to the generalizations of modules to complexes of modules. Some of Professor Iversen's results are given in Chapter 9. Chapter 10 is about Serre's intersection conjecture. The graded case is fully exposed. The last chapter introduces the reader to Fitting ideals and McRae invariants."--
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 512.4 Iv94 (Browse shelf(Opens below)) Available 136018
Total holds: 0

Includes bibliographical references (pages 207-209) and index.

1. Dimension of a local ring--
2. Modules over a local ring--
3.Divisor theory--
4. Completion--
5. Injective modules--
6. Local cohomology--
7. Dualizing complexes--
8. Local duality--
9. Amplitude and dimension--
10. Intersection multiplicities--
11. Complexes of free modules--
Bibliography--
Index.

"The content in Chapter 1-3 is a fairly standard one-semester course on local rings with the goal to reach the fact that a regular local ring is a unique factorization domain. The homological machinery is also supported by Cohen-Macaulay rings and depth. In Chapters 4-6 the methods of injective modules, Matlis duality and local cohomology are discussed. Chapters 7-9 are not so standard and introduce the reader to the generalizations of modules to complexes of modules. Some of Professor Iversen's results are given in Chapter 9. Chapter 10 is about Serre's intersection conjecture. The graded case is fully exposed. The last chapter introduces the reader to Fitting ideals and McRae invariants."--

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