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OverviewThis book is a lightly edited version of the unpublished manuscript Maximal Cohen-Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz.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. Full Product DetailsAuthor: Ragnar-Olaf BuchweitzPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.342kg ISBN: 9781470453404ISBN 10: 1470453401 Pages: 175 Publication Date: 28 February 2022 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsNotations 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 IndexReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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