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Homological Questions in Local Algebra

£56.00

Part of London Mathematical Society Lecture Note Series

  • Date Published: September 1990
  • availability: Available
  • format: Paperback
  • isbn: 9780521315265

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  • 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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    Product details

    • Date Published: September 1990
    • format: Paperback
    • isbn: 9780521315265
    • length: 324 pages
    • dimensions: 228 x 152 x 20 mm
    • weight: 0.455kg
    • availability: Available
  • 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.

  • Author

    Jan R. Strooker

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