Class field theory for strictly quasilocal fields with Henselian discrete valuations

The paper establishes a relationship between finite separable extensions and norm groups of strictly quasilocal fields with Henselian discrete valuations, which yields a generally nonabelian one-dimensional local class field theory.Comment: 14 pages; revised form, to appear in manuscripta mathematica, paper [6] from the list of references has been published in the Proceedings of ICTAMI 05, Alba Iulia, Romania, 15.9-18.9. 2005; Acta Universitatis Apulensis 10/2005, 149-16

On the residue fields of Henselian valued stable fields, II

Let $E$ be a primarily quasilocal field, $M/E$ a finite Galois extension and $D$ a central division $E$-algebra of index divisible by $[M\colon E]$. In addition to the main result of Part I, this part of the paper shows that if the Galois group $G(M/E)$ is not nilpotent, then $M$ does not necessarily embed in $D$ as an $E$-subalgebra. When $E$ is quasilocal, we find the structure of the character group of its absolute Galois group; this enables us to prove that if $E$ is strictly quasilocal and almost perfect, then the divisible part of the multiplicative group $E ^{\ast}$ equals the intersection of the norm groups of finite Galois extensions of $E$.Comment: 10 page