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Singularity categories and Morita equivalence Greenlees, John
Description
(joint with Greg Stevenson) The singularity category of a ring R is defined to be the quotient of the triangulated category of complexes with finitely generated homology modulo the perfect complexes: D_{sg}(R)=D_{fg}(R)/D_{perf}(R). To define the analogue more generally (eg when R is a DGA or a ring spectrum satisfying mild finiteness hypotheses), we need to find analogues of the triangulated categories D_{fg}(R) and D_{perf}(R). The perfect complexes are precisely the small objects, so the denominator is easy. One way to make sense of the finitely generated R-modules is to suppose given a regular ring S and a map S->R making R a small S-module, and take D_{fg}(R) (which may depend on S) to consist of R-modules small over S. This covers interesting cases, and the talk will discuss the use of Morita theory to understand the resulting singularity category.
Item Metadata
Title |
Singularity categories and Morita equivalence
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-06-23T09:01
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Description |
(joint with Greg Stevenson) The singularity category of a ring R is defined to be the quotient of the triangulated category of complexes with finitely generated homology modulo the perfect complexes:
D_{sg}(R)=D_{fg}(R)/D_{perf}(R).
To define the analogue more generally (eg when R is a DGA or a ring spectrum satisfying mild finiteness hypotheses), we need to find analogues of the triangulated categories D_{fg}(R) and D_{perf}(R). The perfect complexes are precisely the small objects, so the denominator is easy. One way to make sense of the finitely generated R-modules is to suppose given a regular ring S and a map S->R making R a small S-module, and take D_{fg}(R) (which may depend on S) to consist of R-modules small over S. This covers interesting cases, and the talk will discuss the use of Morita theory to understand the resulting singularity category.
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Extent |
63 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Sheffield
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Series | |
Date Available |
2016-12-23
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0340429
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International