Description

Book Synopsis
Presents a lightly edited version of the unpublished manuscript Maximal Cohen-Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen-Macaulay modules over (not necessarily commutative) Gorenstein rings.

Table of Contents
  • Notations and conventions
  • Perfect complexes and the stable derived category
  • The category of modules modulo projectives
  • Complete resolutions and the category of acyclic projective complexes
  • Maximal Cohen-Macaulay modules and Gorenstein rings
  • Maximal Cohen-Macaulay approximations
  • The Tate cohomology
  • Multiplicative structure, duality and support
  • First examples
  • Connection to geometry on projective super-spaces
  • Applications to singularities and hypersurfaces
  • Bibliography
  • Comments and errata
  • Gorenstein Noether algebras
  • Subsequent developments
  • Additional bibliography
  • Glossary
  • Index

Maximal CohenMacaulay Modules and Tate Cohomology

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    A Paperback by Ragnar–olaf Buchweitz

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      View other formats and editions of Maximal CohenMacaulay Modules and Tate Cohomology by Ragnar–olaf Buchweitz

      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 2/28/2022 12:00:00 AM
      ISBN13: 9781470453404, 978-1470453404
      ISBN10: 1470453401

      Description

      Book Synopsis
      Presents a lightly edited version of the unpublished manuscript Maximal Cohen-Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen-Macaulay modules over (not necessarily commutative) Gorenstein rings.

      Table of Contents
      • Notations and conventions
      • Perfect complexes and the stable derived category
      • The category of modules modulo projectives
      • Complete resolutions and the category of acyclic projective complexes
      • Maximal Cohen-Macaulay modules and Gorenstein rings
      • Maximal Cohen-Macaulay approximations
      • The Tate cohomology
      • Multiplicative structure, duality and support
      • First examples
      • Connection to geometry on projective super-spaces
      • Applications to singularities and hypersurfaces
      • Bibliography
      • Comments and errata
      • Gorenstein Noether algebras
      • Subsequent developments
      • Additional bibliography
      • Glossary
      • Index

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