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.

中文翻译：

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代数堆栈的 Luna étale 切片定理

我们证明，在具有仿射稳定器的代数封闭域上的每个局部有限类型的代数堆栈，都是具有线性还原稳定器群的点附近的 etale-locally 商堆栈。证明使用了附录中证明的阿廷代数定理的等变版本。我们提供了主要定理的大量应用。