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Title
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Singularity categories via the derived quotient
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Author
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Abstract
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| Given a noncommutative partial resolution A = End(R)(R circle plus M) of a Gorenstein singularity R, we show that the relative singularity category Delta(R) (A) of Kalck-Yang is controlled by a certain connective dga A/(L)AeA, the derived quotient of Braun-Chuang-Lazarev. We think of A/ (L)AeA as a kind of `derived exceptional locus' of the partial resolution A, as we show that it can be thought of as the universal dga fitting into a suitable recollement. This theoretical result has geometric consequences. When R is an isolated hypersurface singularity, it follows that the singularity category Dsg (R) is determined completely by A/(L)AeA, even when A has infinite global dimension. Thus our derived contraction algebra classifies threefold flops, even those X -> Spec(R) where X has only terminal singularities. This gives a solution to the strongest form of the derived Donovan-Wemyss conjecture, which we further show is the best possible classification result in this singular setting. (C) 2021 Elsevier Inc. All rights reserved. |
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Language
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English
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Source (journal)
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Advances in mathematics. - New York, N.Y.
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Publication
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New York, N.Y.
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2021
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ISSN
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0001-8708
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DOI
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10.1016/J.AIM.2021.107631
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Volume/pages
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381
(2021)
, 56 p.
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Article Reference
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107631
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ISI
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000625431200024
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Medium
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E-only publicatie
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Full text (Publisher's DOI)
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Full text (open access)
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Full text (publisher's version - intranet only)
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