A geometric invariant of a finite group

Abstract

We study the class of the classifying stack of a finite group in a Grothendieck group of algebraic stacks introduced previously. We show that this class is trivial in a number of examples most notably for all symmetric groups. We also give some examples where it is not trivial. The latter uses counterexamples of Saltman and Swan to the problem of Noether.

23 pages

References in corpus (1)

• The computation of the classes of some tori in the Grothendieck ring of varieties

Cited by in corpus (10)

• The motive of a classifying space
• The Ekedahl Invariants for finite groups
• The quotient map on the equivariant Grothendieck ring of varieties
• Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve
• Motivic classes of generalized Kummer schemes via relative power structures
• Finite Groups Generated in Low Real Codimension
• On a rationality question in the Grothendieck ring of varieties
• On the pre-lambda ring structure on the Grothendieck ring of stacks and the power structures over it
• Motivic classes of classifying stacks of finite groups and unramified cohomology
• On the Mixed Tate property and the motivic class of the classifying stack of a finite group