Geometricity for derived categories of algebraic stacks

• Daniel Bergh ^[1] ; Valery A. Lunts ^[2] ; Olaf M. Schnürer ^[1]
  1. [1] Universität Bonn
  2. [2] Indiana University
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 4 (Special Issue: The Mathematics of Joseph Bernstein), 2016, págs. 2535-2568
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.