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    Perfect complexes on algebraic stacks

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    Author
    Hall, Jack
    Rydh, David
    Affiliation
    Univ Arizona, Dept Math
    Issue Date
    2017-08-17
    Keywords
    derived categories
    algebraic stacks
    compact generation
    perfect complexes
    
    Metadata
    Show full item record
    Publisher
    CAMBRIDGE UNIV PRESS
    Citation
    Perfect complexes on algebraic stacks 2017, 153 (11):2318 Compositio Mathematica
    Journal
    Compositio Mathematica
    Rights
    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 2017
    ISSN
    0010-437X
    1570-5846
    DOI
    10.1112/S0010437X17007394
    Version
    Final accepted manuscript
    Sponsors
    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_article
    ae974a485f413a2113503eed53cd6c53
    10.1112/S0010437X17007394
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