Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Existence and properties of geometric quotients

Author: David Rydh
Journal: J. Algebraic Geom. 22 (2013), 629-669
Published electronically: May 13, 2013
MathSciNet review: 3084720
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Abstract | References | Additional Information

Abstract: 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 and Mori’s theorem.

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Additional Information

David Rydh
Affiliation: Department of Mathematics, KTH, 100 44 Stockholm, Sweden

Received by editor(s): November 13, 2007
Received by editor(s) in revised form: April 15, 2011
Published electronically: May 13, 2013
Article copyright: © Copyright 2013 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.