Homological Questions in Local Algebra

Homological Questions in Local Algebra

  • Electronic book text
By (author) 

List price: US$89.00

Currently unavailable

We can notify you when this item is back in stock

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks


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.show more

Product details

  • Electronic book text
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 1139242113
  • 9781139242110

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.show more