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On the local quotient structure of Artin stacks

Alper, Jarod


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...[Show more]

CollectionsANU Research Publications
Date published: 2010
Type: Journal article
Source: Journal of Pure and Applied Algebra
DOI: 10.1016/j.jpaa.2009.11.016


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