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arXiv · 1504.06467

A Luna \'etale slice theorem for algebraic stacks

Jarod Alper·Jack Hall·David Rydh
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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.

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Jarod Alper, Jack Hall, David Rydh. 2015-04-24. A Luna \'etale slice theorem for algebraic stacks. https://doi.org/10.4007/annals.2020.191.3.1

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