QUOTIENTS BY GROUPOIDS

@inproceedings{Keel1995QUOTIENTSBG,
  title={QUOTIENTS BY GROUPOIDS},
  author={S. Keel and Shigefumi Mori},
  year={1995}
}
We show that if a flat group scheme acts properly, with finite stabilizers, on an algebraic space, then a quotient exists as a separated algebraic space. More generally we show any flat groupid for which the family of stabilizers is finite has a uniform geometric, uniform categorical quotient in the category of algebraic spaces. Our argument is elementary and essentially self contained. 

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