Geometricity for derived categories of algebraic stacks

We prove that the dg category of perfect complexes on a smooth, proper Deligne–Mumford stack over a field of characteristic zero is geometric in the sense of Orlov, and in particular smooth and proper. On the level of triangulated categories, this means that the derived category of perfect complexes...

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Bibliographic Details
Published in:Selecta mathematica (Basel, Switzerland) Switzerland), 2016-10, Vol.22 (4), p.2535-2568
Main Authors: Bergh, Daniel, Lunts, Valery A., Schnürer, Olaf M.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Sheaves
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Summary:We prove that the dg category of perfect complexes on a smooth, proper Deligne–Mumford stack over a field of characteristic zero is geometric in the sense of Orlov, and in particular smooth and proper. On the level of triangulated categories, this means that the derived category of perfect complexes embeds as an admissible subcategory into the bounded derived category of coherent sheaves on a smooth, projective variety. The same holds for a smooth, projective, tame Artin stack over an arbitrary field.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-016-0280-8