A minimalistic p-adic analog of the Artin-Schreier Theorem

The famous Artin-Schreier Theorem gives a characterization
of the orderings of a field in Galois terms. The corresponding p-adic
Galois situation is well understood too. In this talk I will explain
that the p-adic valuations of any field extension K of a p-adically
closed field can be recovered from the Z/p metabelian Galois theory
of the K. The problem is related and equivalent to the corresponding
p-adic birational section conjecture for arbitrary varieties.