{
  "id": "math/0601686",
  "version": "v1",
  "published": "2006-01-27T19:55:03.000Z",
  "updated": "2006-01-27T19:55:03.000Z",
  "title": "Vojta's Inequality and Rational and Integral Points of Bounded Degree on Curves",
  "authors": [
    "Aaron Levin"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let C in C_1xC_2 be a curve of type (d_1,d_2) in the product of the two curves C_1 and C_2. Let d be a positive integer. We prove that if a certain inequality involving d_1, d_2, d, and the genera of the curves C_1, C_2, and C is satisfied, then the set of points P in C(\\kbar) with [k(P):k]<=d is finite for any number field k. We prove a similar result for integral points of bounded degree on C. These results are obtained as consequences of an inequality of Vojta which generalizes the Roth-Wirsing theorem to curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-27T19:55:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G30",
      "14G40",
      "14H25"
    ],
    "keywords": [
      "integral points",
      "bounded degree",
      "vojtas inequality",
      "number field",
      "similar result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1686L"
    }
  }
}