Shai Keidar (Uni Regensburg)

Title: pi-finite Galois theory

Abstract: In the higher-categorical world, Galois theory extends beyond finite groups: one can study Galois extensions for an arbitrary E_1-group. We develop such a theory for higher semiadditive categories, where finite groups are naturally replaced by pi-finite groups. Under height assumptions, we construct an n-truncated pro-pi-finite “absolute Galois group” representing all Galois extensions, and develop a higher Kummer theory relating abelian extensions to the Picard spectrum. As an illustration, we attach a pro-pi-finite Galois space to a rational Stefanich ring and give an algorithm computing it.