{
  "id": "math/0504303",
  "version": "v2",
  "published": "2005-04-14T18:32:32.000Z",
  "updated": "2006-04-04T14:25:47.000Z",
  "title": "A conjecture on rational approximations to rational points",
  "authors": [
    "David McKinnon"
  ],
  "comment": "49 pages, 3 figures. Exposition improved, particularly in the proofs of the main theorems, and the connection with accumulating subvarieties made explicit",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "In this paper, we examine how well a rational point P on an algebraic variety X can be approximated by other rational points. We conjecture that if P lies on a rational curve, then the best approximations to P on X can be chosen to lie along a rational curve. We prove this conjecture for a wide range of examples, and for a great many more examples we deduce our conjecture from Vojta's Main Conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-04-04T14:25:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05"
    ],
    "keywords": [
      "rational point",
      "rational approximations",
      "rational curve",
      "vojtas main conjecture",
      "algebraic variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4303M"
    }
  }
}