Jan R. Strooker

Homological Questions in Local Algebra (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 6. September 1990
• Englisch
• ISBN-13: 9781139242110
• Artikelnr.: 38277956

Inhaltsangabe

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.