Gorenstein homological algebra and universal coefficient theorems

We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coef...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2017-12, Vol.287 (3-4), p.1109-1155
Main Authors: Dell’Ambrogio, Ivo, Stevenson, Greg, Šťovíček, Jan
Format: Article
Language:English
Subjects:
Coefficients
Homology
Machinery
Mathematics
Mathematics and Statistics
Theorems
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Summary:We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-017-1862-7