Selecta Mathematica

, Volume 22, Issue 4, pp 2535–2568 | Cite as

Geometricity for derived categories of algebraic stacks

  • Daniel Bergh
  • Valery A. Lunts
  • Olaf M. Schnürer
Article

Abstract

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.

Keywords

Differential graded category Derived category Algebraic stack Root construction Semi-orthogonal decomposition 

Mathematics Subject Classification

Primary 14F05 Secondary 14A20 16E45 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Daniel Bergh
    • 1
  • Valery A. Lunts
    • 2
  • Olaf M. Schnürer
    • 1
  1. 1.Mathematisches InstitutUniversität BonnBonnGermany
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

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