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Etale devissage, descent and pushouts of stacks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2505-6417
2011 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 331, no 1, 194-223 p.Article in journal (Refereed) Published
Abstract [en]

We show that the pushout of an kale 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 kale morphisms using such pushouts. We also give a variant of the devissage method for representable quasi-finite flat morphisms.

Place, publisher, year, edition, pages
2011. Vol. 331, no 1, 194-223 p.
Keyword [en]
Etale neighborhood, Distinguished square, Devissage, Descent, Pushout, Algebraic stack, 2-Sheaves
National Category
URN: urn:nbn:se:kth:diva-31871DOI: 10.1016/j.jalgebra.2011.01.006ISI: 000288143700012OAI: diva2:407171
Swedish Research Council
QC 20110329Available from: 2011-03-29 Created: 2011-03-28 Last updated: 2011-03-29Bibliographically approved

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Rydh, David
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