{
  "id": "0711.3645",
  "version": "v1",
  "published": "2007-11-23T18:35:06.000Z",
  "updated": "2007-11-23T18:35:06.000Z",
  "title": "Diophantine Approximation on varieties III: Approximation of non-algebraic points by algebraic points",
  "authors": [
    "Heinrich Massold"
  ],
  "comment": "42 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "For $\\theta$ a non-algebraic point on a quasi projective variety over a number field, I prove that $\\theta$ has an approximation by a series of algebraic points of bounded height and degree which is essentially best possible. Applications of this result will include a proof of a slightly strengthened version of the Philippon criterion, some new algebraic independence criteria, statements concerning metric transcendence theory on varieties of arbitrary dimension, and a rather accurate estimate for the number of algebraic points of bounded height and degree on quasi projective varieties over number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-23T18:35:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J13",
      "11J81",
      "11J85",
      "14G40",
      "14G17",
      "11J83",
      "14J20",
      "11G50",
      "14G25",
      "11G35"
    ],
    "keywords": [
      "algebraic points",
      "non-algebraic point",
      "diophantine approximation",
      "quasi projective variety",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.3645M"
    }
  }
}