Fundamental Group Schemes of some Quot Schemes on a smooth projective curve
Chandranandan Gangopadhyay, Ronnie Sebastian

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 be an algebraically closed field. Let be an irreducible smooth projective curve over . Let be a locally free sheaf on of rank . Fix an integer . Let denote the Quot scheme parameterizing torsion quotients of of degree . In this article we compute the -fundamental group scheme of .
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