Spahn new page Galois theory (changes)

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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

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

Last revised on August 24, 2012 at 17:03:49. See the history of this page for a list of all contributions to it.