{
  "id": "2101.02293",
  "version": "v1",
  "published": "2021-01-06T22:25:17.000Z",
  "updated": "2021-01-06T22:25:17.000Z",
  "title": "Most Elliptic Curves over Global Function Fields are Torsion Free",
  "authors": [
    "Tristan Phillips"
  ],
  "comment": "8 pages. Comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given an elliptic curve $E$ over a global function field $K$, the Galois action on the $n$-torsion points of $E$ gives rise to a mod-n Galois representation $\\rho_{E,n}$. For $K$ satisfying some mild conditions, we show that the set of $E$ for which $\\rho_{E,n}$ is as large as possible for all $n$, has density $1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-06T22:25:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11F80",
      "11N36"
    ],
    "keywords": [
      "global function field",
      "elliptic curve",
      "torsion free",
      "mod-n galois representation",
      "galois action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}