Alper, Hall, Rydh — A Luna Étale Slice Theorem For Algebraic Stacks (2020)

We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is \textasciiacute 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.