Submersions and effective descent of etale morphisms

TL;DR

This paper explores the properties of submersive and subtrusive morphisms, demonstrating their role in effective descent for etale morphisms and extending previous results with applications to geometric quotients.

Contribution

It establishes that universally subtrusive morphisms are of effective descent for etale morphisms, broadening the understanding of morphism properties in algebraic geometry.

Findings

Universally subtrusive morphisms are of effective descent for etale morphisms.

Results extend previous work by Grothendieck, Picavet, and Voevodsky.

Applications include universality of geometric quotients and removing noetherian assumptions.

Abstract

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.