Descente fidèlement plate pour les n -champs d'Artin.

Bertrand Toen (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Domaines: Géométrie algébrique [math.AG]

Bertrand Toen. Descente fidèlement plate pour les n -champs d'Artin.. Compositio Mathematica, 2011, 147 (05), pp.1382-1412. ⟨10.1112/S0010437X10005245⟩. ⟨hal-00772828⟩