the fundamental theorem of Galois theory

(…)

An instance is the following:

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

(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.

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