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Let $k$ be an algebraically closed field of characteristic $p > 3$. Let $X$be an irreducible smooth projective surface over $k$. Fix an integer $n \geq 1$and let ${\mathcal{H}{\it ilb}}_X^n$ be the Hilbert scheme parameterizingeffective $0$-cycles of length $n$ on $X$. The aim of the present article is tofind the $S$-fundamental group scheme and Nori's fundamental group scheme ofthe Hilbert scheme $\mathcal{H}{\it ilb}_X^n$.

Fundamental Group Schemes of Hilbert Scheme of $n$ Points on a Smooth Projective Surface