Perfect complexes on algebraic stacks
dc.contributor.author | Hall, Jack | |
dc.contributor.author | Rydh, David | |
dc.date.accessioned | 2017-11-29T01:59:43Z | |
dc.date.available | 2017-11-29T01:59:43Z | |
dc.date.issued | 2017-08-17 | |
dc.identifier.citation | Perfect complexes on algebraic stacks 2017, 153 (11):2318 Compositio Mathematica | en |
dc.identifier.issn | 0010-437X | |
dc.identifier.issn | 1570-5846 | |
dc.identifier.doi | 10.1112/S0010437X17007394 | |
dc.identifier.uri | http://hdl.handle.net/10150/626173 | |
dc.description.abstract | We 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.sponsorship | Goran Gustafsson Foundation; Australian Research Council [DE150101799]; Swedish Research Council [2011-5599, 2015-05554] | en |
dc.language.iso | en | en |
dc.publisher | CAMBRIDGE UNIV PRESS | en |
dc.relation.url | https://www.cambridge.org/core/product/identifier/S0010437X17007394/type/journal_article | en |
dc.rights | Copyright © The Authors 2017. | en |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | derived categories | en |
dc.subject | algebraic stacks | en |
dc.subject | compact generation | en |
dc.subject | perfect complexes | en |
dc.title | Perfect complexes on algebraic stacks | en |
dc.type | Article | en |
dc.contributor.department | Univ Arizona, Dept Math | en |
dc.identifier.journal | Compositio Mathematica | en |
dc.description.note | 6 month embargo; Published online: 17 August 2017 | en |
dc.description.collectioninformation | This 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.version | Final accepted manuscript | en |
refterms.dateFOA | 2018-02-17T00:00:00Z | |
html.description.abstract | We 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. |