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 $\Gal_k$.

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- Last edited by Bjorn Poonen on 2022-03-24 15:40:29

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- 2022-03-24 15:40:29 by Bjorn Poonen (Reviewed)