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arXiv · 0704.1557

On the residue fields of Henselian valued stable fields, II

I. D. Chipchakov
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Abstract

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 $E$.

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I. D. Chipchakov. 2007-04-12. On the residue fields of Henselian valued stable fields, II. https://arxiv.org/abs/0704.1557

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