absolute Galois group
Cohomology and Extensions
The absolute Galois group of a field is that of the field extension which is the separable closure of . When is a perfect field this is equivalently the Galois group of the algebraic closure .
An instance of Grothendieck's Galois theory is the following:
from the category of étale schemes to the category of sets equipped with an action of the absolute Galois group is an equivalence of categories.
Of the rational numbers
- Jakob Stix, The Grothendieck-Teichmüller group and Galois theory of the rational numbers, 2004 (pdf)
Discussion of the p-adic absolute Galois group as the etale fundamental group of a quotient of some perfectoid space is in
Revised on May 21, 2015 11:32:55
by Urs Schreiber