On Some Finiteness Questions for Algebraic Stacks

On Some Finiteness Questions for Algebraic Stacks

We prove that under a certain mild hypothesis, the DG category of D-modules on a quasi-compact algebraic stack is compactly generated. We also show that under the same hypothesis, the functor of global sections on the DG category of quasi-coherent sheaves is continuous.

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Veröffentlicht in:Geometric and functional analysis 2013-02, Vol.23 (1), p.149-294
Hauptverfasser: Drinfeld, Vladimir, Gaitsgory, Dennis
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematics
Mathematics and Statistics
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Zusammenfassung:We prove that under a certain mild hypothesis, the DG category of D-modules on a quasi-compact algebraic stack is compactly generated. We also show that under the same hypothesis, the functor of global sections on the DG category of quasi-coherent sheaves is continuous.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-012-0204-5