The Nori fundamental gerbe of tame stacks

TL;DR

This paper investigates the relationship between the Nori fundamental group of a tame algebraic stack and its coarse moduli space, exploring conditions for uniformization by algebraic spaces.

Contribution

It provides a comparison between the Nori fundamental groups of tame stacks and their coarse moduli spaces, and studies uniformization conditions.

Findings

Established conditions for when a tame stack can be uniformized by an algebraic space.

Compared Nori fundamental groups of stacks and their coarse moduli spaces.

Identified cases where the Nori fundamental group of the stack differs from that of its coarse moduli space.

Abstract

Given an algebraic stack, we compare its Nori fundamental group with that of its coarse moduli space. We also study conditions under which the stack can be uniformized by an algebraic space.