2007/10/31 by David Rydh · 1 citation
Mathematics · #math.AG #math.AC #msc:14A15 #msc:13B21 #msc:13B22 #msc:13B40 #msc:14F20 #msc:14F43
paper · pdf · doi:10.24033/bsmf.2588
published as Bull. Soc. Math. France 138 (2), 2010, p. 181-230 · 42 pages; added sections on descent of locally closed subsets and weakly normal descent; many other changes; final version
arxiv created 2010/03/05 · arxiv updated 2019/05/07
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.