Homological Questions in Local Algebra
Homological Questions in Local Algebra
£58.99
GBPThis 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.
Product details
May 2012Adobe eBook Reader
9781139242110
0 pages
0kg
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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
- 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.
