A Luna \'etale slice theorem for algebraic stacks
Algebraic Geometry
2021-01-19 v3
Abstract
We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is \'etale-locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group. The proof uses an equivariant version of Artin's algebraization theorem proved in the appendix. We provide numerous applications of the main theorems.
Keywords
Cite
@article{arxiv.1504.06467,
title = {A Luna \'etale slice theorem for algebraic stacks},
author = {Jarod Alper and Jack Hall and David Rydh},
journal= {arXiv preprint arXiv:1504.06467},
year = {2021}
}
Comments
47 pages, reorganization of results and applications, corrected applications to Bialynicki-Birula decompositions and equivariant versal deformations for curves, additional material added throughout, final version