Title: Detecting the Remains of Valuations in Small Pro-ell Galois Groups

Abstract:
The existence of valuations of a field K force very precise
relations in its absolute Galois group. In several situations, these
special relations can be used to detect valuations from the
group-theoretical structure of the absolute Galois group. Indeed,
detecting valuations from Galois groups has been the key first step in
several results in birational anabelian geometry. In this talk, I will
explain how one can detect precisely which relations in
almost-abelian quotients of the pro-ell Galois group come from
valuations. As a consequence, I will explain how these
``almost-abelian'' relations force non-trivial restrictions on the
structure of the full pro-ell Galois group.