{
  "id": "2010.01130",
  "version": "v1",
  "published": "2020-10-02T17:56:21.000Z",
  "updated": "2020-10-02T17:56:21.000Z",
  "title": "Tamely ramified morphisms of curves and Belyi's theorem in positive characteristic",
  "authors": [
    "Kiran S. Kedlaya",
    "Daniel Litt",
    "Jakub Witaszek"
  ],
  "comment": "23 pages, comments welcome",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We show that every smooth projective curve over a finite field k admits a finite tame morphism to the projective line over k. Furthermore, we construct a curve with no such map when k is an infinite perfect field of characteristic two. Our work leads to a refinement of the tame Belyi theorem in positive characteristic, building on results of Sa\\\"idi, Sugiyama-Yasuda, and Anbar-Tutdere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-02T17:56:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G17"
    ],
    "keywords": [
      "tamely ramified morphisms",
      "positive characteristic",
      "belyis theorem",
      "finite tame morphism",
      "infinite perfect field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}