Recovering fields from small quotients of their absolute Galois groups
Florian Pop
In this talk we will consider function fields K of dimension > 1 over
algebraic closures k of finite fields. We will show how to recover K, in
a functorial way, from the maximal abelian-by-central pro-l quotient of
the absolute Galois group of K. This solves a problem posed by Bogomolov
in 1990, in the case of such base fields.