This book presents an account of several conjectures arising in commutative algebra from the pioneering work of Serre and Auslander-Buchsbaum. The approach is via Hochster's 'Big Cohen-Macaulay modules', though the complementary view point of Peskine-Szpiro and Roberts, who study the homology of certain complexes, is not neglected. Various refinements of Hochster's construction, obtained in collaboration with Bartijn, are included. A special feature is a long chapter written by Van den Dries which explains how a certain type of result can be 'lifted' from prime characteristic to characteristic zero. Though this is primarily a research monograph, it does provide introductions to most of the topics treated. Non-experts may therefore find it an appealing guide into an active area of algebra.
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- Date Published: September 1990
- format: Paperback
- isbn: 9780521315265
- length: 324 pages
- dimensions: 228 x 152 x 20 mm
- weight: 0.455kg
- availability: Available
Table of Contents
1. Homological preliminaries
2. Adic topologies and completions
3. Injective envelopes and minimal injective resolutions
4. Local cohomology and koszul complexes
5. (Pre-) Regular sequences and depth
6. Exactness of complexes and linear equations over rings
7. Comparing homological invariants
9. Cohen-Macauley modules and regular rings
10. Gorenstein rings, local duality, and the direct summand conjecture
11. Frobenius and big Cohen-Macauley modules
12. Big Cohen-Macaulay modules in equal charecteristic 0
13. Uses of big Cohen-Maculay Modules.
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