Homological Questions in Local Algebra

This book presents an account of several conjectures arising in commutative algebra from the pioneering work of Serre and Auslander-Buchsbaum.

Jan R. Strooker (Author)

9780521315265, Cambridge University Press

Paperback, published 6 September 1990

324 pages
22.8 x 15.2 x 2 cm, 0.455 kg

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.

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.

Subject Areas: Algebra [PBF]