{
  "id": "2308.01683",
  "version": "v1",
  "published": "2023-08-03T10:50:27.000Z",
  "updated": "2023-08-03T10:50:27.000Z",
  "title": "Growth of Torsion Groups of Elliptic Curves Upon Base Change from Quadratic Fields",
  "authors": [
    "Bo-Hae Im",
    "Hansol Kim"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For a quadratic field $\\mathcal{K}$ without rationally defined CM, we prove that there exists of a prime $p_{\\mathcal{K}}$ depending only on $\\mathcal{K}$ such that if $d$ is a positive integer whose minimal prime divisor is greater than $p_{\\mathcal{K}}$, then for any extension $L/\\mathcal{K}$ of degree d and any elliptic curve $E/\\mathcal{K}$, we have $E\\left(L\\right)_{\\operatorname{tors}} = E\\left(\\mathcal{K}\\right)_{\\operatorname{tors}}$. By not assuming the GRH, this is a generalization of the results by Genao, and Gon\\'alez-Jim\\'enez and Najman.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-03T10:50:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic field",
      "elliptic curve",
      "base change",
      "torsion groups",
      "minimal prime divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}