A Luna étale slice theorem for algebraic stacks

Jarod Alper, Jack Hall, David Rydh

Published 2015-04-24Version 1

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.