Birger Iversen and Holger Andreas Nielsen, "Lecture Notes on Local Rings"
English | ISBN: 9814603651 | 2014 | 213 pages | PDF | 1 MB
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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