{
  "id": "1802.02958",
  "version": "v1",
  "published": "2018-02-08T16:46:43.000Z",
  "updated": "2018-02-08T16:46:43.000Z",
  "title": "Deligne's conjecture for automorphic motives over CM-fields, Part I: factorization",
  "authors": [
    "Harald Grobner",
    "Michael Harris",
    "Jie Lin"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "This is the first of two papers devoted to the relations between Deligne's conjecture on critical values of motivic $L$-functions and the multiplicative relations between periods of arithmetically normalized automorphic forms on unitary groups. The present paper combines the Ichino-Ikeda-Neal Harris (IINH) formula with an analysis of cup products of coherent cohomological automorphic forms on Shimura varieties to establish relations between certain automorphic periods and critical values of Rankin-Selberg and Asai $L$-functions of $GL(n)\\times GL(m)$ over CM fields. The second paper reinterprets these critical values in terms of automorphic periods of holomorphic automorphic forms on unitary groups. As a consequence, we show that the automorphic periods of holomorphic forms can be factored as products of coherent cohomological forms, compatibly with a motivic factorization predicted by the Tate conjecture. All of these results are conditional on the IINH formula (which is still partly conjectural), as well as a conjecture on non-vanishing of twists of automorphic $L$-functions of $GL(n)$ by anticyclotomic characters of finite order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-08T16:46:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F70",
      "11G18",
      "11R39",
      "22E55"
    ],
    "keywords": [
      "delignes conjecture",
      "automorphic motives",
      "automorphic periods",
      "critical values",
      "factorization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}