# 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

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.

Revised on June 7, 2012 19:44:50 by Stephan Alexander Spahn (79.227.183.2)