On the local quotient structure of Artin stacks

Details On the local quotient structure of Artin stacks On the local quotient structure of Artin stacks

2009-04-14

arxiv.org/abs/0904.2050v3

J. Pure Appl. Algebra 214 (2010), no. 9, 1576-1591

Mathematics

Algebraic Geometry

23 pages, this version agrees with the published version with an error in Proposition 6.8 fixed

Scientific paper

We show that near closed points with linearly reductive stabilizer, Artin stacks are formally locally quotient stacks by the stabilizer. We conjecture that the statement holds etale locally and we provide some evidence for this conjecture. In particular, we prove that if the stabilizer of a point is linearly reductive, the stabilizer acts algebraically on a miniversal deformation space generalizing results of Pinkham and Rim.

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