Publisher
CAMBRIDGE UNIV PRESSCitation
Perfect complexes on algebraic stacks 2017, 153 (11):2318 Compositio MathematicaJournal
Compositio MathematicaRights
Copyright © The Authors 2017.Collection Information
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.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.Note
6 month embargo; Published online: 17 August 2017ISSN
0010-437X1570-5846
Version
Final accepted manuscriptSponsors
Goran Gustafsson Foundation; Australian Research Council [DE150101799]; Swedish Research Council [2011-5599, 2015-05554]Additional Links
https://www.cambridge.org/core/product/identifier/S0010437X17007394/type/journal_articleae974a485f413a2113503eed53cd6c53
10.1112/S0010437X17007394