Homological questions in local algebra
著者
書誌事項
Homological questions in local algebra
（London Mathematical Society lecture note series, 145）
Cambridge University Press, 1990
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注記
Bibliography: p. [297]-308
内容説明・目次
内容説明
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.
目次
- 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.
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