Pro-ℓ abelian-by-central Galois theory of prime divisors

In the present paper it is shown that one can recover much of the inertia structure of (quasi) divisors of a function field K|k over an algebraically closed base field k from the maximal pro-l abelian-by-central Galois theory of K. The results play a central role in the birational anabelian geometry and related questions.