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Perfect complexes on algebraic stacks
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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 To\"en 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.
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Cited by 1 Pith paper
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A class of perverse schobers in Geometric Invariant Theory
For any quasi-symmetric representation of a reductive group, the derived categories of GIT quotients form a perverse schober on the partial compactification of the stringy Kähler moduli space.
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