Étale dévissage, descent and pushouts of stacks

By David Rydh. 2010

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Abstract We show that the pushout of an etale morphism and an open immersion exists in the category of algebraic stacks and show that such pushouts behave similarly to the gluing of two open substacks. For example, quasi-coherent sheaves on the pushout can be described by a simple gluing procedure. We then outline a powerful devissage method for representable etale morphisms using such pushouts. We also give a variant of the devissage method for representable quasi-finite flat morphisms.

Subfields: Geometry and Topology, History, Literature and Literary Theory

View Paper: https://www.semanticscholar.org/paper/8f5d86eca9dd84f6a7d1a690b880e3d7d18673c3