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Maximal Cohen–Macaulay Modules and Tate Cohomology
 
Edited by: Luchezar L. Avramov University of Nebraska, Lincoln, NE
Benjamin Briggs University of Utah, Salt Lake City, UT
Srikanth B. Iyengar University of Utah, Salt Lake City, UT
Janina C. Letz Bielefeld University, Bielefeld, Germany

With appendices by Luchezar L. Avramov, Benjamin Briggs, Srikanth B. Iyengar, and Janina C. Letz.

Maximal Cohen--Macaulay Modules and Tate Cohomology
Softcover ISBN:  978-1-4704-5340-4
Product Code:  SURV/262
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-6792-0
Product Code:  SURV/262.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-5340-4
eBook: ISBN:  978-1-4704-6792-0
Product Code:  SURV/262.B
List Price: $250.00 $187.50
MAA Member Price: $225.00 $168.75
AMS Member Price: $200.00 $150.00
Maximal Cohen--Macaulay Modules and Tate Cohomology
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Maximal Cohen–Macaulay Modules and Tate Cohomology
Edited by: Luchezar L. Avramov University of Nebraska, Lincoln, NE
Benjamin Briggs University of Utah, Salt Lake City, UT
Srikanth B. Iyengar University of Utah, Salt Lake City, UT
Janina C. Letz Bielefeld University, Bielefeld, Germany

With appendices by Luchezar L. Avramov, Benjamin Briggs, Srikanth B. Iyengar, and Janina C. Letz.

Softcover ISBN:  978-1-4704-5340-4
Product Code:  SURV/262
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-1-4704-6792-0
Product Code:  SURV/262.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-5340-4
eBook ISBN:  978-1-4704-6792-0
Product Code:  SURV/262.B
List Price: $250.00 $187.50
MAA Member Price: $225.00 $168.75
AMS Member Price: $200.00 $150.00
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2622021; 175 pp
    MSC: Primary 13; 16; 18

    This book is a lightly edited version of the unpublished manuscript Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz.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. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.

    Readership

    Graduate students and researchers interested in commutative algebra, category theory, and applications to quantum field theory.

  • Table of Contents
     
     
    • Chapters
    • 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
    • Comments and errata
    • Gorenstein Noether algebras
    • Subsequent developments
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2622021; 175 pp
MSC: Primary 13; 16; 18

This book is 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. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.

Readership

Graduate students and researchers interested in commutative algebra, category theory, and applications to quantum field theory.

  • Chapters
  • 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
  • Comments and errata
  • Gorenstein Noether algebras
  • Subsequent developments
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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