Perfect complexes on algebraic stacks
Abstract
We develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks that either have finite stabilizers or are local quotient stacks. We also extend To\"en and Antieau--Gepner's results on derived Azumaya algebras and compact generation of sheaves on linear categories from derived schemes to derived Deligne--Mumford stacks. These are all consequences of our main theorem: compact generation of a presheaf of triangulated categories on an algebraic stack is local for the quasi-finite flat topology.
Cite
@article{arxiv.1405.1887,
title = {Perfect complexes on algebraic stacks},
author = {Jack Hall and David Rydh},
journal= {arXiv preprint arXiv:1405.1887},
year = {2019}
}
Comments
reordering of the Introduction and sections 3 and 4; additional material on perfect complexes; Appendix A on Mayer--Vietoris squares incorporated into arXiv:1606.08517; final version, to appear in Compositio Math