Dao, H, Faber, E orcid.org/0000-0003-2541-8916 and Ingalls, C (2015) Noncommutative (Crepant) Desingularizations and the Global Spectrum of Commutative Rings. Algebras and Representation Theory, 18 (3). pp. 633-664. ISSN 1386-923X
Abstract
In this paper we study endomorphism rings of finite global dimension over not necessarily normal commutative rings. These objects have recently attracted attention as noncommutative (crepant) resolutions, or NC(C)Rs, of singularities. We propose a notion of a NCCR over any commutative ring that appears weaker but generalizes all previous notions. Our results yield strong necessary and sufficient conditions for the existence of such objects in many cases of interest. We also give new examples of NCRs of curve singularities, regular local rings and normal crossing singularities. Moreover, we introduce and study the global spectrum of a ring R, that is, the set of all possible finite global dimensions of endomorphism rings of MCM R-modules. Finally, we use a variety of methods to compute global dimension for many endomorphism rings.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014, Springer Science+Business Media Dordrecht. This is a post-peer-review, pre-copyedit version of an article published in Algebras and Representation Theory. The final authenticated version is available online at: https:// doi.org/10.1007/s10468-014-9510-y. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Noncommutative (crepant) resolutions; Rational singularities; Global spectrum; Endomorphism rings |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 Jul 2018 12:53 |
Last Modified: | 25 Jun 2023 21:24 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s10468-014-9510-y |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132504 |