Spahn
new page Galois theory

Galois connections

Galois theory of fields

Galois theory of schemes

Theorem

(fundamental theorem of Galois theory?)

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

The functor

{k.Sch etGal(k s/k)Mod XX(k s)\begin{cases} k.Sch_{et}\to Gal(k_s / k)- Mod \\ X\mapsto X(k_s) \end{cases}

from étale k-schemes? to the category of Galois modules Gal(k s/s)ModGal(k_s/s)-Mod is an equivalence of categories. Here Gal(k s/k)Gal (k_s/k) is considered as a profinite topological group.

Demazure, section I.8, p.17

Grothendieck’s Galois theory

Galois descend

References