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arXiv · 2407.10511

Okutsu sequences in Henselian fields

Enric Nart
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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-Vaqui\'e chains of the natural valuation on $K[x]$ induced by $\theta$.

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Enric Nart. 2024-07-15. Okutsu sequences in Henselian fields. https://arxiv.org/abs/2407.10511

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