Nori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors

Abstract

We prove the existence of a Galois closure for towers of torsors under finite group schemes over a proper, geometrically connected and geometrically reduced algebraic stack X over a field k. This is done by describing the Nori fundamental gerbe of an essentially finite cover of X. A similar result is also obtained for the S -fundamental gerbe.