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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Cambridge University Press
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Worked examples or Exercises
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ISBN-13
978-1-139-24211-0 (9781139242110)
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Schweitzer Klassifikation
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; 8. Dimensions; 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.
