Definition 53.6.1. 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

$\pi _1(X, \overline{x}) = \text{Aut}(F_{\overline{x}})$

of automorphisms of the fibre functor $F_{\overline{x}} : \textit{FÉt}_ X \to \textit{Sets}$ endowed with its canonical profinite topology from Lemma 53.3.1.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).