Submersions and effective descent of etale morphisms

Details Submersions and effective descent of etale morphisms Submersions and effective descent of etale morphisms

2007-10-12

arxiv.org/abs/0710.2488v3

Bull. Soc. Math. France 138 (2), 2010, p. 181-230

Mathematics

Algebraic Geometry

42 pages; added sections on descent of locally closed subsets and weakly normal descent; many other changes; final version

Scientific paper

Using the flatification by blow-up result of Raynaud and Gruson, we obtain new results for submersive and subtrusive morphisms. We show that universally subtrusive morphisms, and in particular universally open morphisms, are morphisms of effective descent for the fibered category of etale morphisms. Our results extend and supplement previous treatments on submersive morphisms by Grothendieck, Picavet and Voevodsky. Applications include the universality of geometric quotients and the elimination of noetherian hypotheses in many instances.

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