{
  "id": "2312.07710",
  "version": "v1",
  "published": "2023-12-12T20:15:43.000Z",
  "updated": "2023-12-12T20:15:43.000Z",
  "title": "The classifying element for quotients of Fermat curves",
  "authors": [
    "Juanita Duque-Rosero",
    "Rachel Pries"
  ],
  "comment": "2 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "Suppose $C$ is a cyclic Galois cover of the projective line branched at the three points $0$, $1$, and $\\infty$. Under a mild condition on the ramification, we determine the structure of the graded Lie algebra of the lower central series of the fundamental group of $C$ in terms of a basis which is well-suited to studying the action of the absolute Galois group of $\\mathbb{Q}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-12T20:15:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D41",
      "11G32",
      "14F35",
      "14H30",
      "17B70",
      "11F06",
      "11F67",
      "11G30",
      "13A50",
      "14F20"
    ],
    "keywords": [
      "fermat curves",
      "classifying element",
      "absolute galois group",
      "cyclic galois cover",
      "lower central series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}