A separable closure of a field 
is a separable algebraic
extension 
having no nontrivial finite separable extensions. Inside
a fixed algebraic closure, it is the subfield
of all elements separable over 
. It is unique up to 
-isomorphism, but that isomorphism
is generally not unique. In characteristic
zero, every algebraic extension is separable,
so the separable closure equals the algebraic closure.
For example, 
is a separable closure of 
.
The absolute Galois group is 
. Its maximal pro-
quotient is used in the Bogomolov-Pop reconstruction assertion.
