{
  "id": "2101.01858",
  "version": "v1",
  "published": "2021-01-06T03:55:38.000Z",
  "updated": "2021-01-06T03:55:38.000Z",
  "title": "Extensions of local fields given by 3-term Eisenstein polynomials",
  "authors": [
    "Endrit Fejzullahu",
    "Kevin Keating"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be a local field with residue characteristic $p$ and let $L/K$ be a totally ramified extension of degree $p^k$. In this paper we show that if $L/K$ has only two distinct indices of inseparability then there exists a uniformizer $\\pi_L$ for $L$ whose minimum polynomial over $K$ has at most three terms. This leads to an explicit classification of extensions with two indices of inseparability. Our classification extends work of Amano, who considered the case $k=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-06T03:55:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S05"
    ],
    "keywords": [
      "local field",
      "eisenstein polynomials",
      "classification extends work",
      "explicit classification",
      "residue characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}