{
  "id": "2109.09301",
  "version": "v1",
  "published": "2021-09-20T05:22:28.000Z",
  "updated": "2021-09-20T05:22:28.000Z",
  "title": "Universality of the Galois action on the fundamental group of $\\mathbb{P}^1\\setminus\\{0,1,\\infty\\}$",
  "authors": [
    "Alexander Petrov"
  ],
  "comment": "comments welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove that any semi-simple representation of the Galois group of a number field coming from geometry appears as a subquotient of the ring of regular functions on the pro-algebraic completion of the fundamental group of the projective line with $3$ punctures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-20T05:22:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F35",
      "11F80"
    ],
    "keywords": [
      "fundamental group",
      "galois action",
      "universality",
      "galois group",
      "pro-algebraic completion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}