AffiliationUniv Arizona, Dept Math
MetadataShow full item record
PublisherCAMBRIDGE UNIV PRESS
CitationPerfect complexes on algebraic stacks 2017, 153 (11):2318 Compositio Mathematica
RightsCopyright © The Authors 2017
Collection InformationThis 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 email@example.com.
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.
Note6 month embargo; Published online: 17 August 2017
VersionFinal accepted manuscript
SponsorsGoran Gustafsson Foundation; Australian Research Council [DE150101799]; Swedish Research Council [2011-5599, 2015-05554]