{
  "id": "2405.03612",
  "version": "v1",
  "published": "2024-05-06T16:31:11.000Z",
  "updated": "2024-05-06T16:31:11.000Z",
  "title": "Fields of definition of dynamical systems on $\\mathbb{P}^{1}$. Improvements on a result of Silverman",
  "authors": [
    "Giulio Bresciani"
  ],
  "categories": [
    "math.NT",
    "math.AG",
    "math.DS"
  ],
  "abstract": "J. Silverman proved that a dynamical system on $\\mathbb{P}^{1}$ descends to the field of moduli if it is polynomial or it has even degree, but for non-polynomial ones of odd degree the picture is less clear. We give a complete characterization of which dynamical systems over $\\mathbb{P}^{1}$ descend to the field of moduli.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-06T16:31:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamical system",
      "definition",
      "improvements",
      "complete characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}