Geometricity for derived categories of algebraic stacks
Algebraic Geometry
2018-08-14 v2
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.
Cite
@article{arxiv.1601.04465,
title = {Geometricity for derived categories of algebraic stacks},
author = {Daniel Bergh and Valery A. Lunts and Olaf M. Schnürer},
journal= {arXiv preprint arXiv:1601.04465},
year = {2018}
}
Comments
31 pages