The motivic class of the classifying stack of the special orthogonal group

TL;DR

This paper calculates the class of the classifying stack of the special orthogonal group within the Grothendieck ring of stacks, confirming it equals the inverse of the group's class, advancing understanding in algebraic geometry.

Contribution

It provides an explicit computation of the class of the classifying stack for the special orthogonal group, a novel result in the Grothendieck ring context.

Findings

The class of the classifying stack equals the inverse of the group's class.

The computation confirms a conjectured relation in the Grothendieck ring.

This work enhances the understanding of algebraic stacks and their classes.

Abstract

We compute the class of the classifying stack of the special orthogonal group in the Grothendieck ring of stacks, and check that it is equal to the multiplicative inverse of the class of the group.