consisting just of those automorphisms of whose restriction to is the identity is called Galois group of the field extension .
The just defined Galois group is the one occurring in the classical Galois theory for fields. The analog of the Galois group in Galois theory for schemes is a fundamental group (of a scheme) and is rarely called a ”Galois group”.
The Galois group of the separable closure of is called the absolute Galois group of . In this case we have is equivalent to the fundamental group of the scheme . In particular the notion of fundamental group (of a point of) a topos generalizes that of Galois group. This observation is the starting point and motivating example of Grothendieck's Galois theory and more generally of that of homotopy groups in an (infinity,1)-topos.