Fundamental Group Schemes of some Quot Schemes on a smooth projective curve

TL;DR

This paper computes the $S$-fundamental group scheme of a Quot scheme parameterizing torsion quotients of a locally free sheaf on a smooth projective curve over an algebraically closed field.

Contribution

It provides the first computation of the $S$-fundamental group scheme for these specific Quot schemes, extending understanding of their algebraic fundamental groups.

Findings

Explicit description of the $S$-fundamental group scheme of the Quot scheme.

New insights into the structure of fundamental group schemes of moduli spaces.

Connections between the geometry of Quot schemes and their fundamental group schemes.

Abstract

Let $k$ be an algebraically closed field. Let $C$ be an irreducible smooth projective curve over $k$. Let $E$ be a locally free sheaf on $C$ of rank $\geq 2$. Fix an integer $d \geq 2$. Let $\mathcal{Q}$ denote the Quot scheme parameterizing torsion quotients of $E$ of degree $d$. In this article we compute the $S$-fundamental group scheme of $\mathcal{Q}$.