Algebraic and Nori fundamental gerbes

TL;DR

This paper extends the concept of algebraic fundamental groups to fibered categories using gerbes, providing a Tannakian interpretation for the Nori fundamental gerbe in broader algebraic stack contexts.

Contribution

It generalizes the algebraic fundamental group to fibered categories via gerbes and offers a Tannakian perspective for the Nori fundamental gerbe in non-smooth, non-pseudo-proper stacks.

Findings

Extended the algebraic fundamental group to fibered categories

Provided a Tannakian interpretation for the Nori fundamental gerbe

Applicable to non-smooth, non-pseudo-proper algebraic stacks

Abstract

In this paper we extend the generalized algebraic fundamental group constructed by Esnault and Hogadi to general fibered categories using the language of gerbes. As an application we obtain a Tannakian interpretation for the Nori fundamental gerbe defined by Borne and Vistoli for non smooth non pseudo-proper algebraic stacks.