Okutsu sequences in Henselian fields

Abstract

For $(K,v)$ a Henselian valued field, let $\theta \in \overline{K}$ with minimal polynomial $F$ over $K$. Okutsu sequences of $\theta$ have been defined only when the extension $K(\theta )/K$ is defectless. In this paper, we extend this concept to arbitrary $\theta \in \overline{K}$ and we show that these objects are essentially equivalent to Okutsu frames of $F$ and to Mac Lane-Vaquié chains of the natural valuation on $K[x]$ induced by $\theta$.