Abstract
We study the local properties of Artin stacks and their good moduli spaces, if they exist. We show that near closed points with linearly reductive stabilizer, Artin stacks formally locally admit good moduli spaces. In particular, the geometric invariant theory is developed for actions of linearly reductive group schemes on formal affine schemes. We also give conditions for when the existence of good moduli spaces can be deduced from the existence of étale charts admitting good moduli spaces.
Citation
Jarod Alper. "Local properties of good moduli spaces." Tohoku Math. J. (2) 64 (1) 105 - 123, 2012. https://doi.org/10.2748/tmj/1332767342
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