Spahn new page Galois theory (Rev #1, changes)

Showing changes from revision #0 to #1: Added | ~~Removed~~ | ~~Chan~~ged

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

Revision on August 22, 2012 at 13:46:28 by Stephan Alexander Spahn?. See the history of this page for a list of all contributions to it.