A Luna etale slice theorem for algebraic stacks

• 成果类型: Article
• 署名作者: Alper, Jarod; Hall, Jack; Rydh, David
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.191.3.1
• 发表日期: 2020
• 页码: 675-738
• 关键词: bialynicki-birula decomposition; MODULI SPACES; linearization; approximation; generation; CATEGORIES; schemes; Duality; MAPS

摘要

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