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May 2020 A Luna étale slice theorem for algebraic stacks
Jarod Alper, Jack Hall, David Rydh
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Ann. of Math. (2) 191(3): 675-738 (May 2020). DOI: 10.4007/annals.2020.191.3.1

Abstract

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.

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Jarod Alper. Jack Hall. David Rydh. "A Luna étale slice theorem for algebraic stacks." Ann. of Math. (2) 191 (3) 675 - 738, May 2020. https://doi.org/10.4007/annals.2020.191.3.1

Information

Published: May 2020
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2020.191.3.1

Subjects:
Primary: 14D23
Secondary: 14B12 , 14L24 , 14L30

Keywords: algebraic stacks , equivariant geometry , moduli spaces , quotients

Rights: Copyright © 2020 Department of Mathematics, Princeton University

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Vol.191 • No. 3 • May 2020
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