Definition 57.6.1. Let $X$ be a connected scheme. Let $\overline{x}$ be a geometric point of $X$. The *fundamental group* of $X$ with *base point* $\overline{x}$ is the group

of automorphisms of the fibre functor $F_{\overline{x}} : \textit{FÉt}_ X \to \textit{Sets}$ endowed with its canonical profinite topology from Lemma 57.3.1.

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