Flat descent for Artin n-stacks

Details Flat descent for Artin n-stacks Flat descent for Artin n-stacks

2009-11-18

arxiv.org/abs/0911.3554v2

Mathematics

Algebraic Geometry

French, 28 pages. Minor changes

Scientific paper

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.

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