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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.10511 |
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| _version_ | 1866916324370808832 |
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| author | Nart, Enric |
| author_facet | Nart, Enric |
| contents | For $(K,v)$ a Henselian valued field, let $θ\in\overline{K}$ with minimal polynomial $F$ over $K$. Okutsu sequences of $θ$ have been defined only when the extension $K(θ)/K$ is defectless. In this paper, we extend this concept to arbitrary $θ\in\overline{K}$ 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 $θ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Okutsu sequences in Henselian fields Nart, Enric Number Theory Commutative Algebra For $(K,v)$ a Henselian valued field, let $θ\in\overline{K}$ with minimal polynomial $F$ over $K$. Okutsu sequences of $θ$ have been defined only when the extension $K(θ)/K$ is defectless. In this paper, we extend this concept to arbitrary $θ\in\overline{K}$ 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 $θ$. |
| title | Okutsu sequences in Henselian fields |
| topic | Number Theory Commutative Algebra |
| url | https://arxiv.org/abs/2407.10511 |