Let k be an algebraically closed field of characteristic $p>3$. Let X be an irreducible smooth projective surface over k. Fix an integer $n\ge 2$ and let $\mathcal{H}{\mathit{ilb}}_X^n$ be the Hilbert scheme parameterizing effective 0-cycles of length n on X. The aim of the present article is to find the S-fundamental group scheme and Nori's fundamental group scheme of the Hilbert scheme $\mathcal{H}{\mathit{ilb}}_X^n$.

中文翻译：

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光滑投影面上n个点的希尔伯特方案的基本群方案

令k为特征的代数封闭场$p>3$。令X为k上不可约的光滑射影曲面。固定整数$ñ\ge 2$ 然后让 $\mathcal{H}{\mathit{b}}_X^{ñ}$是在X上参数化长度为n的有效0周期的希尔伯特方案。本文的目的是找到希尔伯特方案的S-基群方案和Nori基本群方案$\mathcal{H}{\mathit{b}}_X^{ñ}$。