Anneaux de 'polynômes à valeurs entières' et anneaux de Fatou
Asymptotic behaviour of monomial ideals on regular sequences.
Presentation depth and the Lipman-Sathaye Jacobian theorem.
Submersions and effective descent of étale morphisms
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 étale 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...