Existence of quotients by finite groups and coarse moduli spaces

Details Existence of quotients by finite groups and coarse moduli spaces Existence of quotients by finite groups and coarse moduli spaces

2007-08-24

arxiv.org/abs/0708.3333v1

Mathematics

Algebraic Geometry

34 pages

Scientific paper

In this paper we prove the existence of several quotients in a very general setting. We consider finite group actions and more generally groupoid actions with finite stabilizers generalizing the results of Keel and Mori. In particular we show that any algebraic stack with finite inertia stack has a coarse moduli space. We also show that any algebraic stack with quasi-finite diagonal has a locally quasi-finite flat cover. The proofs do not use noetherian methods and are valid for general algebraic spaces and algebraic stacks.

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