On the Brauer $p$-dimension of Henselian discrete valued fields of residual characteristic $p>0$

Abstract

Let $(K,v)$ be a Henselian discrete valued field with residue field $\hat{K}$ of characteristic $p$, and Brd${}_p(K)$ be the Brauer $p$-dimension of $K$. This paper shows that Brd${}_p(K)\ge n$, if $[\hat{K}:{\hat{K}}^p]=p^n$, for some $n\in \mathbb{N}$. It proves that Brd${}_p(K)=\infty$ if and only if $[\hat{K}:{\hat{K}}^p]=\infty$.

26 pages, no figures. Final form: the content of the paper is the same as in the previous version; the titles of Sections 5 and 6 are changed because of the changes in the content of these sections, made in the previous version. To appear in J. Pure Appl. Algebra

References in corpus (3)

• Period-index and u-invariant questions for function fields over complete discretely valued fields
• On the behaviour of Brauer $p$-dimensions under finitely-generated field extensions
• On Brauer $p$-dimensions and index-exponent relations over finitely-generated field extensions