Perfect complexes on algebraic stacks

Jack Hall, David Rydh

Research output: Contribution to journalArticle

9 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2318-2367
Number of pages50
JournalCompositio Mathematica
Volume153
Issue number11
DOIs
StatePublished - Nov 1 2017

Keywords

  • Kyewords derived categories
  • algebraic stacks
  • compact generation
  • perfect complexes

ASJC Scopus subject areas

  • Algebra and Number Theory

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