{
  "id": "2204.13275",
  "version": "v1",
  "published": "2022-04-28T04:08:30.000Z",
  "updated": "2022-04-28T04:08:30.000Z",
  "title": "Ramification of Tate modules for rank $2$ Drinfeld modules",
  "authors": [
    "Takuya Asayama",
    "Maozhou Huang"
  ],
  "comment": "25 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we study the ramification of extensions of a function field generated by division points of rank $2$ Drinfeld modules. Also conductors of certain rank $2$ Drinfeld modules are defined as analogues of those for elliptic curves. A calculation of these conductors allows us to show an analogue of Szpiro conjecture under a certain limited situation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-28T04:08:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G09",
      "11S15",
      "11S20",
      "11F80"
    ],
    "keywords": [
      "drinfeld modules",
      "tate modules",
      "ramification",
      "szpiro conjecture",
      "division points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}