{
  "id": "math/0209177",
  "version": "v1",
  "published": "2002-09-14T19:49:39.000Z",
  "updated": "2002-09-14T19:49:39.000Z",
  "title": "On the periods of motives with complex multiplication and a conjecture of Gross-Deligne",
  "authors": [
    "V. Maillot",
    "D. Roessler"
  ],
  "comment": "20 pages, submitted",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove that the existence of an automorphism of finite order on a (defined over a number field) variety X implies the existence of algebraic linear relations between the logarithm of certain periods of X and the logarithm of special values of the Gamma-function. This implies that a slight variation of results by Anderson, Colmez and Gross on the periods of CM abelian varieties is valid for a larger class of CM motives. In particular, we prove a weak form of the period conjecture of Gross-Deligne. Our proof relies on the arithmetic fixed point formula (equivariant arithmetic Riemann-Roch theorem) proved by K. Koehler and the second author, and the vanishing of the equivariant analytic torsion for the Dolbeault complex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-09-14T19:49:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R42",
      "14K22",
      "14K20",
      "14C30",
      "14C40",
      "14G40"
    ],
    "keywords": [
      "complex multiplication",
      "conjecture",
      "gross-deligne",
      "equivariant arithmetic riemann-roch theorem",
      "equivariant analytic torsion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9177M"
    }
  }
}