A Luna etale slice theorem for algebraic stacks

Jarod Alper; Jack Hall; David Rydh

doi:10.4007/annals.2020.191.3.1

A Luna etale slice theorem for algebraic stacks

Jarod Alper
, Jack Hall
, David Rydh

Mathematics

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

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.

Original language	English (US)
Pages (from-to)	675-738
Number of pages	64
Journal	Annals of Mathematics
Volume	191
Issue number	3
DOIs	https://doi.org/10.4007/annals.2020.191.3.1
State	Published - May 2020

Keywords

Algebraic stacks
Equivariant geometry
Moduli spaces
Quotients

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.4007/annals.2020.191.3.1

Cite this

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AB - 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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KW - Equivariant geometry

KW - Moduli spaces

KW - Quotients

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A Luna etale slice theorem for algebraic stacks

Abstract

Keywords

ASJC Scopus subject areas

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