{
  "id": "1302.2944",
  "version": "v3",
  "published": "2013-02-12T22:57:25.000Z",
  "updated": "2014-12-30T18:11:56.000Z",
  "title": "Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves",
  "authors": [
    "Jennifer S. Balakrishnan",
    "Amnon Besser",
    "J. Steffen Müller"
  ],
  "comment": "27 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use the method in explicit computation. An important aspect of the method is that it only requires a basis of the Mordell-Weil group tensored with the rationals.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-05T21:10:47.000Z",
      "title": "p-adic height pairings and integral points on hyperelliptic curves",
      "comment": "26 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-12-30T18:11:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S80",
      "14G40",
      "11Y50",
      "11G30",
      "11D41"
    ],
    "keywords": [
      "p-adic height pairing",
      "hyperelliptic curve",
      "p-integral points",
      "mordell-weil rank",
      "finding p-adic approximations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.2944B"
    }
  }
}