Tohoku Mathematical Journal
2012
March
SECOND SERIES VOL. 64, NO. 1

Tohoku Math. J.
64 (2012), 105-123

Title LOCAL PROPERTIES OF GOOD MODULI SPACES

Author Jarod Alper

(Received November 9, 2009, revised March 31, 2011)
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.

2000 Mathematics Subject Classification. Primary 14D23; Secondary 13A50.
Key words and phrases. Artin stacks, good moduli spaces, invariant theory.

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