Motivic classes of classifying stacks of finite groups and unramified cohomology

Abstract

Combining work of Peyre, Colliot-Thélène and Voisin, we give the first example of a finite group $G$ such that the motivic class of its classifying stack $BG$ in Ekedahl's Grothendieck ring of stacks over $\mathbb{C}$ is non-trivial and $BG$ has trivial unramified Brauer group.

References in corpus (4)

• The Grothendieck group of algebraic stacks
• The motive of a classifying space
• A geometric invariant of a finite group
• The Ekedahl Invariants for finite groups