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dc.contributor.authorHall, Jack
dc.contributor.authorRydh, David
dc.date.accessioned2017-11-29T01:59:43Z
dc.date.available2017-11-29T01:59:43Z
dc.date.issued2017-08-17
dc.identifier.citationPerfect complexes on algebraic stacks 2017, 153 (11):2318 Compositio Mathematicaen
dc.identifier.issn0010-437X
dc.identifier.issn1570-5846
dc.identifier.doi10.1112/S0010437X17007394
dc.identifier.urihttp://hdl.handle.net/10150/626173
dc.description.abstractWe develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks that either have finite stabilizers or are local quotient stacks. We also extend Toën and Antieau–Gepner’s results on derived Azumaya algebras and compact generation of sheaves on linear categories from derived schemes to derived Deligne–Mumford stacks. These are all consequences of our main theorem: compact generation of a presheaf of triangulated categories on an algebraic stack is local for the quasi-finite flat topology.
dc.description.sponsorshipGoran Gustafsson Foundation; Australian Research Council [DE150101799]; Swedish Research Council [2011-5599, 2015-05554]en
dc.language.isoenen
dc.publisherCAMBRIDGE UNIV PRESSen
dc.relation.urlhttps://www.cambridge.org/core/product/identifier/S0010437X17007394/type/journal_articleen
dc.rightsCopyright © The Authors 2017en
dc.subjectderived categoriesen
dc.subjectalgebraic stacksen
dc.subjectcompact generationen
dc.subjectperfect complexesen
dc.titlePerfect complexes on algebraic stacksen
dc.typeArticleen
dc.contributor.departmentUniv Arizona, Dept Mathen
dc.identifier.journalCompositio Mathematicaen
dc.description.note6 month embargo; Published online: 17 August 2017en
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en
dc.eprint.versionFinal accepted manuscripten
refterms.dateFOA2018-02-17T00:00:00Z
html.description.abstractWe develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks that either have finite stabilizers or are local quotient stacks. We also extend Toën and Antieau–Gepner’s results on derived Azumaya algebras and compact generation of sheaves on linear categories from derived schemes to derived Deligne–Mumford stacks. These are all consequences of our main theorem: compact generation of a presheaf of triangulated categories on an algebraic stack is local for the quasi-finite flat topology.


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