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

TL;DR

This paper establishes the existence of Galois closures for towers of torsors over algebraic stacks by describing the Nori fundamental gerbe of essentially finite covers, extending fundamental group concepts to more complex geometric structures.

Contribution

It introduces a method to construct Galois closures for towers of torsors using the Nori fundamental gerbe, generalizing classical Galois theory to algebraic stacks.

Findings

Existence of Galois closure for towers of torsors under finite group schemes.

Description of the Nori fundamental gerbe for essentially finite covers.

Extension of results to the $S$-fundamental gerbe.

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.