Geometric component (reviewed)

A geometric component of a smooth scheme $X$ of finite type over a field $k$ is an irreducible component of the base change $X_{\overline{k}}$. (Because $X_{\overline{k}}$ is smooth, irreducible components are the same as connected components.)

The set $\pi_0(X_{\overline{k}})$ of geometric components is a finite set with an action of the absolute Galois group $\Gal_k$.