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the fundamental theorem of Galois theory

(…)

An instance is the following:

Let kk be a field, let k sk_s denote the separable closure of kk.

Theorem

(fundamental theorem of Galois theory)

The functor

{Sch etGal(k s/k)Mod XX(k s)\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)ModGal(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)