On index-exponent relations over Henselian fields with local residue fields

Abstract

Let $p$ be a prime number and $(K,v)$ a Henselian valued field with a residue field $\hat{K}$. This paper determines the Brauer $p$-dimension of $K$, in case $p\ne \mathrm{char}(\hat{K})$ and $\hat{K}$ is a $p$-quasilocal field properly included in its maximal $p$-extension. When $\hat{K}$ is a local field, it describes index-exponent pairs of central division $K$-algebras of $p$-primary degrees. The same goal is achieved, if $(K,v)$ is maximally complete, char$(K)=p$ and $\hat{K}$ is local.

21 pages, LaTeX. Final form: to appear in Serdica Mathematical Journal

References in corpus (1)

• On the behaviour of Brauer $p$-dimensions under finitely-generated field extensions