{
  "id": "2411.06745",
  "version": "v1",
  "published": "2024-11-11T06:54:15.000Z",
  "updated": "2024-11-11T06:54:15.000Z",
  "title": "Arboreal Galois groups of postcritically finite quadratic polynomials",
  "authors": [
    "Robert L. Benedetto",
    "Dragos Ghioca",
    "Jamie Juul",
    "Thomas J. Tucker"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We provide an explicit construction of the arboreal Galois group for the postcritically finite polynomial $f(z) = z^2 +c$, where $c$ belongs to some arbitrary field of characteristic not equal to $2$. In this first of two papers, we consider the case that the critical point is periodic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-11T06:54:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arboreal galois group",
      "postcritically finite quadratic polynomials",
      "postcritically finite polynomial",
      "arbitrary field",
      "explicit construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}