{
  "id": "1807.02823",
  "version": "v1",
  "published": "2018-07-08T14:04:30.000Z",
  "updated": "2018-07-08T14:04:30.000Z",
  "title": "From Picard groups of hyperelliptic curves to class groups of quadratic fields",
  "authors": [
    "Jean Gillibert"
  ],
  "comment": "28 pages, LaTeX",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $C$ be a hyperelliptic curve defined over $\\mathbb{Q}$, whose Weierstrass points are defined over extensions of $\\mathbb{Q}$ of degree at most three, and at least one of them is rational. Generalizing a result of R. Soleng (in the case of elliptic curves), we prove that any line bundle of degree $0$ on $C$ which is not torsion can be specialised into ideal classes of imaginary quadratic fields whose order can be made arbitrarily large. This gives a positive answer, for such curves, to a question by Agboola and Pappas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-08T14:04:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Gxx"
    ],
    "keywords": [
      "hyperelliptic curve",
      "class groups",
      "picard groups",
      "imaginary quadratic fields",
      "weierstrass points"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}