SUBMERSIONS AND EFFECTIVE DESCENT OF ETALE MORPHISMS

摘要

Using the fiatification 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.