2009/11/18 by Bertrand Toën, B. Toen, Toen, B.
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #math.CT
paper · pdf · doi:10.48550/arxiv.0911.3554
French, 28 pages. Minor changes
openalex publication_date 2009/11/18 · arxiv created 2010/01/07 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.