Maximal Cohen-Macaulay modules and Tate cohomology
著者
書誌事項
Maximal Cohen-Macaulay modules and Tate cohomology
（Mathematical surveys and monographs, v. 262）
American Mathematical Society, c2021
- : pbk
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注記
Includes bibliographical references (p. 155-165) and index
内容説明・目次
内容説明
This book is a lightly edited version of the unpublished manuscript Maximal Cohen-Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz.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.
目次
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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