Quotients by Groupoids
Copyright policy )Quotients by Groupoids
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.
AMSTeX
- Kyoto University Japan
categorical quotient, Homogeneous spaces and generalizations, algebraic group actions, Group actions on varieties or schemes (quotients), Generalizations (algebraic spaces, stacks), Mathematics - Algebraic Geometry, Geometric invariant theory, FOS: Mathematics, algebraic spaces, Algebraic Geometry (math.AG), geometric quotients
categorical quotient, Homogeneous spaces and generalizations, algebraic group actions, Group actions on varieties or schemes (quotients), Generalizations (algebraic spaces, stacks), Mathematics - Algebraic Geometry, Geometric invariant theory, FOS: Mathematics, algebraic spaces, Algebraic Geometry (math.AG), geometric quotients
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