English

Flat descent for Artin n-stacks

Algebraic Geometry 2010-01-07 v2 Category Theory

Abstract

We prove two flat descent statements for Artin n-stacks. We first show that an n-stack for the etale topology which is an Artin n-stack in the sense of HAGII, is also an n-stack for the fppf topology. Moreover, an n-stack for the fppf topology which possess a fppf n-atlas is an Artin n-stack (i.e. possesses a smooth n-atlas). We deduce from these results some comparison statements between fppf and etale (non-ablelian) cohomolgies. This paper is written in the setting of derived algebraic geometry and its results are also valid for derived Artin n-stacks.

Cite

@article{arxiv.0911.3554,
  title  = {Flat descent for Artin n-stacks},
  author = {B. Toen},
  journal= {arXiv preprint arXiv:0911.3554},
  year   = {2010}
}

Comments

French, 28 pages. Minor changes

R2 v1 2026-06-21T14:13:14.092Z