{
  "id": "1604.05197",
  "version": "v1",
  "published": "2016-04-18T15:08:31.000Z",
  "updated": "2016-04-18T15:08:31.000Z",
  "title": "p-adic uniformization and the action of Galois on certain affine correspondences",
  "authors": [
    "Patrick Ingram"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Given two monic polynomials f and g with coefficients in a number field K, and some a in K, we examine the action of the absolute Galois group of K on the directed graph of iterated preimages of a under the correspondence g(y)=f(x), assuming that deg(f)>deg(g) and that gcd(deg(f), deg(g))=1. If a prime of K exists at which f and g have integral coefficients, and at which a is not integral, we show that this directed graph of preimages consists of finitely many Galois-orbits. We obtain this result by establishing a p-adic uniformization of such correspondences, tenuously related to Bottcher's uniformization of polynomial dynamical systems over the complex numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-18T15:08:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P20",
      "11S20"
    ],
    "keywords": [
      "p-adic uniformization",
      "affine correspondences",
      "absolute galois group",
      "directed graph",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160405197I"
    }
  }
}