Finitely generated pro-p Galois groups of p-Henselian fields Original Research Article

Let p be a prime number, let K be a field of characteristic 0 containing a primitive root of unity of order p. Also let v be a p-henselian (Krull) valuation on K with residue characteristic p. We determine the structure of the maximal pro-p Galois group GK(p) of K, provided that it is finitely generated. This extends classical results of Demuimagekin, Serre and Labute.