{
  "id": "2009.01414",
  "version": "v1",
  "published": "2020-09-03T02:05:33.000Z",
  "updated": "2020-09-03T02:05:33.000Z",
  "title": "Diophantine geometry and Serre C*-algebras",
  "authors": [
    "Igor Nikolaev"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT",
    "math.OA"
  ],
  "abstract": "Let $V(k)$ be projective variety over a number field $k$ and let $K$ be a finite extension of $k$. We classify the $K$-isomorphisms of $V(k)$ in terms of the Serre $C^*$-algebra of $V(k)$. As an application, a new proof of the Faltings Finiteness Theorem for the rational points on the higher genus curves is suggested.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-03T02:05:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35",
      "14A22",
      "46L85"
    ],
    "keywords": [
      "diophantine geometry",
      "faltings finiteness theorem",
      "higher genus curves",
      "number field",
      "finite extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}