Existence and properties of geometric quotients
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.
Cite
@article{arxiv.0708.3333,
title = {Existence and properties of geometric quotients},
author = {David Rydh},
journal= {arXiv preprint arXiv:0708.3333},
year = {2013}
}
Comments
36 pages; the proof of the existence of quasi-finite flat presentations has been excluded (now in 1005.2171); quasi-separatedness assumptions dropped; some parts have been reorganized; title changed from "Existence of quotients by finite groups and coarse moduli spaces"