A Luna étale slice theorem for algebraic stacks
By Jarod Alper, Jack Hall, David Rydh. 2015
152 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7f378c81c814278f8e2a8fd75b802e00fd8ebda6
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In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Coherent Tannaka duality and algebraicity of Hom-stacks (2014, methodology): “em 1.1 is a consequence of Theorem 8.4, which also gives various refinements in the non-noetherian situation and when X has quasi-affine or quasi-finite diagonal. Main applications. In work with J. Alper [AHR15], Theorem 1.1 is applied to resolve Alper’s conjecture on the local quotient structure of alg”