A Luna étale slice theorem for algebraic stacks


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


Jarod Alper

Department of Mathematics, University of Washington, Seattle, WA, USA

Jack Hall

University of Arizona, Tucson, AZ and School of Mathematics & Statistics, The University of Melbourne, Parkville, Australia

David Rydh

Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden