#### Vol. 6, No. 1, 2012

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The Chevalley–Shephard–Todd theorem for finite linearly reductive group schemes

### Matthew Satriano

Vol. 6 (2012), No. 1, 1–26
##### Abstract

We generalize the classical Chevalley–Shephard–Todd theorem to the case of finite linearly reductive group schemes. As an application, we prove that every scheme $X$ which is étale-locally the quotient of a smooth scheme by a finite linearly reductive group scheme is the coarse space of a smooth tame Artin stack (as defined by Abramovich, Olsson, and Vistoli), whose stacky structure is supported on the singular locus of $X$.

##### Keywords
Chevalley–Shephard–Todd, pseudoreflection, linearly reductive, tame stacks
Primary: 14A20
Secondary: 14L15