Gorenstein homological algebra and universal coefficient theorems

Dell’Ambrogio, I., Stevenson, G. and Šťovíček, J. (2017) Gorenstein homological algebra and universal coefficient theorems. Mathematische Zeitschrift, 287(3-4), pp. 1109-1155. (doi: 10.1007/s00209-017-1862-7)

Abstract

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.

• Item Type: Articles
• Additional Information: Ivo Dell’Ambrogio is partially supported by the Labex CEMPI (ANR-11-LABX-0007-01). Greg Stevenson is grateful to the Alexander von Humboldt Stiftung for their support. Jan Štovícek was supported by Grant GACR P201/12/G028 from the Czech Science Foundation.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Stevenson, Dr Gregory
• Authors: Dell’Ambrogio, I., Stevenson, G., and Šťovíček, J.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Mathematische Zeitschrift
• Publisher: Springer
• ISSN: 0025-5874
• ISSN (Online): 1432-1823
• Published Online: 24 February 2017
• Copyright Holders: Copyright © 2017 Springer-Verlag Berlin Heidelberg
• First Published: First published in Mathematische Zeitschrift 287(3-4):1109-1155
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher