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
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/