On the local quotient structure of Artin stacks
Algebraic Geometry
2017-12-12 v4
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 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.
Keywords
Cite
@article{arxiv.0904.2050,
title = {On the local quotient structure of Artin stacks},
author = {Jarod Alper},
journal= {arXiv preprint arXiv:0904.2050},
year = {2017}
}
Comments
23 pages, this version agrees with the published version with errors in 2.7 and 6.8 fixed