nLab the fundamental theorem of Galois theory

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An instance is the following:

Let $k$ be a field, let $k_s$ denote the separable closure of $k$.

Theorem

(fundamental theorem of Galois theory)

The functor

$$\begin{cases} Sch_{et}\to Gal(k_s / k)- Mod \\ X\mapsto X(k_s) \end{cases}$$

from étale schemes to the category of Galois modules $Gal(k_s/s)-Mod$ is an equivalence of categories.