Almost-Commuting-Liftable Subgroups of Galois Groups

Abstract

Let K be a field and \ell be a prime such that char K \neq \ell. In the presence of sufficiently many roots of unity in K, we show how to recover some of the inertia/decomposition structure of valuations inside the maximal (\Z/\ell)-abelian resp. pro-\ell-abelian Galois group of K using its (Z/\ell)-central resp. pro-\ell-central extensions.

Version 2: updated two references, added a few words to the argument in Theorem 3, fixed a few typos. All results and arguments are the same. 38 pages