{
  "id": "1910.04653",
  "version": "v1",
  "published": "2019-10-10T15:35:46.000Z",
  "updated": "2019-10-10T15:35:46.000Z",
  "title": "Explicit quadratic Chabauty over number fields",
  "authors": [
    "Jennifer S. Balakrishnan",
    "Amnon Besser",
    "Francesca Bianchi",
    "J. Steffen Müller"
  ],
  "comment": "33 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We generalize the explicit quadratic Chabauty techniques for integral points on odd degree hyperelliptic curves and for rational points on genus 2 bielliptic curves to arbitrary number fields using restriction of scalars. This is achieved by combining equations coming from Siksek's extension of classical Chabauty with equations defined in terms of p-adic heights attached to independent continuous idele class characters. We give several examples to show the practicality of our methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-10T15:35:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G30",
      "11S80",
      "11Y50",
      "14G40"
    ],
    "keywords": [
      "odd degree hyperelliptic curves",
      "explicit quadratic chabauty techniques",
      "independent continuous idele class characters",
      "arbitrary number fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}