Spahn new page Galois theory

Galois connections

Galois theory of fields

Galois theory of schemes

Theorem

(fundamental theorem of Galois theory?)

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

The functor

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

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

Demazure, section I.8, p.17

Grothendieck’s Galois theory

Galois descend

References

• Demazure, Lectures on p-divisible group?

• Grothendieck's Galois theory

• Richard Taylor, IAS, Galois representations, pdf

• George Janelidze, Walter Tholen, extended Galois theory and dissonant morphisms

• John Baez, week 201