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Existence and properties of geometric quotients
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2505-6417
2013 (English)In: Journal of Algebraic Geometry, ISSN 1056-3911, E-ISSN 1534-7486, Vol. 22, no 4, 629-669 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we study quotients of groupoids and coarse moduli spaces of stacks in a general setting. Geometric quotients are not always categorical, but we present a natural topological condition under which a geometric quotient is categorical. We also show the existence of geometric quotients of finite flat groupoids and give explicit local descriptions. Exploiting similar methods, we give an easy proof of the existence of quotients of flat groupoids with finite stabilizers. As the proofs do not use Noetherian methods and are valid for general algebraic spaces and algebraic stacks, we obtain a slightly improved version of Keel andMori's theorem.

Place, publisher, year, edition, pages
2013. Vol. 22, no 4, 629-669 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-140034DOI: 10.1090/S1056-3911-2013-00615-3ISI: 000344048900002Scopus ID: 2-s2.0-84885676763OAI: oai:DiVA.org:kth-140034DiVA: diva2:689628
Note

QC 20140121

Available from: 2014-01-21 Created: 2014-01-16 Last updated: 2017-12-06Bibliographically approved

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Rydh, David

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