{
  "id": "2101.07507",
  "version": "v1",
  "published": "2021-01-19T08:36:14.000Z",
  "updated": "2021-01-19T08:36:14.000Z",
  "title": "On Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms",
  "authors": [
    "Shih-Yu Chen"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2012.00625",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms. We extend the result of Morimoto based on generalization and refinement of the results of Grobner and Lin to cohomological irreducible essentially conjugate self-dual cuspidal automorphic representations of ${\\rm GL}_2$ and ${\\rm GL}_3$ over CM-fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-19T08:36:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert modular forms",
      "symmetric fourth",
      "delignes conjecture",
      "essentially conjugate self-dual cuspidal",
      "irreducible essentially conjugate self-dual"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}