{
  "id": "0801.4459",
  "version": "v4",
  "published": "2008-01-29T09:48:23.000Z",
  "updated": "2010-03-16T14:43:23.000Z",
  "title": "Integral Points on Hyperelliptic Curves",
  "authors": [
    "Y. Bugeaud",
    "M. Mignotte",
    "S. Siksek",
    "M. Stoll",
    "Sz. Tengely"
  ],
  "journal": "Algebra & Number Theory 2 (2008), No. 8, 859-885.",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a completely explicit upper bound for integral points on (standard) affine models of hyperelliptic curves, provided we know at least one rational point and a Mordell-Weil basis of the Jacobian. We also explain a powerful refinement of the Mordell--Weil sieve which, combined with the upper bound, is capable of determining all the integral points. Our method is illustrated by determining the integral points on a two genus 2 hyperelliptic curves with Mordell--Weil Jacobian ranks of 3 and 6.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-03-16T14:43:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G30",
      "11J86"
    ],
    "keywords": [
      "integral points",
      "hyperelliptic curves",
      "explicit upper bound",
      "mordell-weil jacobian ranks",
      "affine models"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.4459B"
    }
  }
}