{
  "id": "2107.05514",
  "version": "v1",
  "published": "2021-07-12T15:38:14.000Z",
  "updated": "2021-07-12T15:38:14.000Z",
  "title": "A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so",
  "authors": [
    "Levent Alpöge",
    "Manjul Bhargava",
    "Ari Shnidman"
  ],
  "comment": "14 pages, comments welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We show that a positive proportion of quartic fields are not monogenic, despite having no local obstruction to being monogenic. Our proof builds on the corresponding result for cubic fields that we obtained in a previous work. Along the way, we also prove that a positive proportion of quartic rings of integers do not arise as the invariant order of an integral binary quartic form despite having no local obstruction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-12T15:38:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R16",
      "11R45"
    ],
    "keywords": [
      "local obstruction",
      "positive proportion",
      "quartic fields",
      "integral binary quartic form despite",
      "cubic fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}