Groups of automorphisms of local fields of period p and nilpotent class < p, II.

Abstract

Suppose KK is a finite field extension of Qpℚp containing a primitive ppth root of unity. Let Γ<pΓ<p be the maximal quotient of period pp and nilpotent class <p<p of the Galois group of a maximal pp-extension of KK. We describe the ramification filtration {Γ(v)<p}v≥0{Γ<p(v)}v≥0 and relate it to an explicit form of the Demushkin relation for Γ<pΓ<p. The results are given in terms of Lie algebras attached to the appropriate pp-groups by the classical equivalence of the categories of pp-groups and Lie algebras of nilpotent class <p<p.