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

Satriano, Matthew

doi:10.2140/ant.2012.6.1

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

Matthew Satriano

Vol. 6 (2012), No. 1, 1–26

DOI: 10.2140/ant.2012.6.1

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

Mathematical Subject Classification 2000

Primary: 14A20

Secondary: 14L15

Milestones

Received: 20 April 2010

Revised: 26 December 2010

Accepted: 24 January 2011

Published: 15 June 2012

Authors

Matthew Satriano
Department of Mathematics University of Michigan 530 Church St. Ann Arbor, MI 48109-1043 United States
http://www-personal.umich.edu/~satriano/

Vol. 6, No. 1, 2012