On the local quotient structure of Artin stacks
Date
2010
Authors
Alper, Jarod
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Elsevier
Abstract
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 �tale 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 the results of Pinkham and Rim. We provide a generalization and stack-theoretic proof of Luna�s �tale slice theorem which shows that GIT quotient stacks are �tale locally quotients stacks by the stabilizer.
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Journal of Pure and Applied Algebra
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Journal article
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2037-12-31
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