{
  "id": "1804.01800",
  "version": "v2",
  "published": "2018-04-05T12:15:36.000Z",
  "updated": "2018-09-13T11:46:06.000Z",
  "title": "On geometry of the ring of algebraic integers",
  "authors": [
    "Igor Nikolaev"
  ],
  "comment": "8 pages, 1 figure; an update",
  "categories": [
    "math.NT",
    "math.AG",
    "math.OA"
  ],
  "abstract": "We study geometry of the ring of algebraic integers $O_K$ of a number field $K$. Namely, it is proved that the inclusion $\\mathbf{Z}\\subset O_K$ defines a covering of the Riemann sphere $\\mathbf{C}P^1$ ramified over three points $\\{0,1,\\infty\\}$. Our approach is based on the notion of a Serre $C^*$-algebra. As an application, a new short proof of the Belyi Theorem is given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-09-13T11:46:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "14H55",
      "46L85"
    ],
    "keywords": [
      "algebraic integers",
      "belyi theorem",
      "study geometry",
      "short proof",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}