{
  "id": "1303.3809",
  "version": "v2",
  "published": "2013-03-15T15:36:35.000Z",
  "updated": "2014-01-13T16:55:21.000Z",
  "title": "A local-global principle for isogenies of prime degree over number fields",
  "authors": [
    "Samuele Anni"
  ],
  "comment": "22 pages, presentation improved as suggested by the referees. To appear in Journal of London Mathematical Society. arXiv admin note: text overlap with arXiv:1006.1782 by other authors",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a description of the set of exceptional pairs for a number field $K$, that is the set of pairs $(\\ell, j(E))$, where $\\ell$ is a prime and $j(E)$ is the $j$-invariant of an elliptic curve $E$ over $K$ which admits an $\\ell$-isogeny locally almost everywhere but not globally. We obtain an upper bound for $\\ell$ in such pairs in terms of the degree and the discriminant of $K$. Moreover, we prove finiteness results about the number of exceptional pairs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-13T16:55:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11G05",
      "14H52",
      "14K02",
      "14G05",
      "14G35"
    ],
    "keywords": [
      "number field",
      "prime degree",
      "local-global principle",
      "exceptional pairs",
      "elliptic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.3809A"
    }
  }
}