{
  "id": "1010.3393",
  "version": "v2",
  "published": "2010-10-17T02:59:27.000Z",
  "updated": "2011-02-12T16:07:48.000Z",
  "title": "A finiteness result for post-critically finite polynomials",
  "authors": [
    "Patrick Ingram"
  ],
  "comment": "Version 2: several errors have been corrected, and some new material added. The inequalities in the main result have changed slightly",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "We show that the set of complex points in the moduli space of polynomials of degree d corresponding to post-critically finite polynomials is a set of algebraic points of bounded height. It follows that for any B, the set of conjugacy classes of post-critically finite polynomials of degree d with coefficients of algebraic degree at most B is a finite and effectively computable set. In the case d=3 and B=1 we perform this computation. The proof of the main result comes down to finding a relation between the \"naive\" height on the moduli space, and Silverman's critical height.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-12T16:07:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "post-critically finite polynomials",
      "finiteness result",
      "moduli space",
      "main result comes",
      "conjugacy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.3393I"
    }
  }
}