Mathematics – Algebraic Geometry
Scientific paper
2010-05-12
Mathematics
Algebraic Geometry
33 pages
Scientific paper
We show that the push-out of an etale morphism and an open immersion exists in the category of algebraic stacks and show that such push-outs behave similarly to the gluing of two open substacks. For example, quasi-coherent sheaves on the push-out can be described by a simple gluing procedure. We then outline a powerful devissage method for representable etale morphisms using such push-outs. We also give a variant of the devissage method for representable quasi-finite flat morphisms.
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