{
  "id": "math/0608427",
  "version": "v3",
  "published": "2006-08-16T14:23:37.000Z",
  "updated": "2007-11-26T15:05:30.000Z",
  "title": "On Davenport-Stothers inequalities and elliptic surfaces in positive characteristic",
  "authors": [
    "Matthias Schuett",
    "Andreas Schweizer"
  ],
  "comment": "24 pages, 1 table; v3: refereed version with minor changes; some typos corrected and section 2 extended",
  "journal": "Quarterly J. Math. 59 (2008), 499-522",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We show that the Davenport-Stothers inequality from characteristic 0 fails in any characteristic p>3. The proof uses elliptic surfaces over the projective line and inseparable base change. We then present adjusted inequalities. These follow from results of Pesenti-Szpiro. For characteristic 2 and 3, we achieve a similar result in terms of the maximal singular fibres of elliptic surfaces over the projective line. Our ideas are also related to supersingular surfaces (in Shioda's sense).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-11-26T15:05:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J27",
      "11G05",
      "12E10"
    ],
    "keywords": [
      "elliptic surfaces",
      "davenport-stothers inequality",
      "positive characteristic",
      "projective line",
      "maximal singular fibres"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8427S"
    }
  }
}