The Galois theory of $G$-spectra and the Burnside ring

Abstract

We prove that the Galois groupoid of the category of $G$-spectra for a finite group $G$ is algebraic, i.e. equivalent to the \'etale fundamental groupoid of the Burnside ring of $G$. We implement an algorithm that computes the latter from the table of marks of $G$, and provide numerous examples.