{
  "id": "math/0212324",
  "version": "v2",
  "published": "2002-12-23T17:55:40.000Z",
  "updated": "2004-09-23T19:58:05.000Z",
  "title": "On complex and noncommutative tori",
  "authors": [
    "Igor Nikolaev"
  ],
  "comment": "13 pages, straighten version, to appear Proc. Amer. Math. Soc",
  "journal": "Proc. Amer. Math. Soc. 134 (2006), 973-981",
  "doi": "10.1090/S0002-9939-05-08244-4",
  "categories": [
    "math.AG",
    "math.OA"
  ],
  "abstract": "The \"noncommutative geometry\" of complex algebraic curves is studied. As first step, we clarify a morphism between elliptic curves, or complex tori, and C*-algebras T_t={u,v | vu=exp(2\\pi it)uv}, or noncommutative tori. The main result says that under the morphism isomorphic elliptic curves map to the Morita equivalent noncommutative tori. Our approach is based on the rigidity of the length spectra of Riemann surfaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-09-23T19:58:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H52",
      "46L85"
    ],
    "keywords": [
      "morphism isomorphic elliptic curves map",
      "complex algebraic curves",
      "morita equivalent noncommutative tori",
      "main result says",
      "riemann surfaces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....12324N"
    }
  }
}