{
  "id": "2407.10511",
  "version": "v1",
  "published": "2024-07-15T08:07:12.000Z",
  "updated": "2024-07-15T08:07:12.000Z",
  "title": "Okutsu sequences in Henselian fields",
  "authors": [
    "Enric Nart"
  ],
  "categories": [
    "math.NT",
    "math.AC"
  ],
  "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 $\\theta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-15T08:07:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "okutsu sequences",
      "henselian fields",
      "mac lane-vaquie chains",
      "natural valuation",
      "okutsu frames"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}