{
  "id": "1512.08929",
  "version": "v1",
  "published": "2015-12-30T13:02:40.000Z",
  "updated": "2015-12-30T13:02:40.000Z",
  "title": "Companions on Artin stacks",
  "authors": [
    "Weizhe Zheng"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Deligne's conjecture that $\\ell$-adic sheaves on normal schemes over a finite field admit $\\ell'$-companions was proved by Lafforgue in the case of curves and by Drinfeld in the case of smooth schemes. In this paper, we extend Drinfeld's theorem to smooth Artin stacks and to their coarse moduli spaces. In contrast to the case of smooth schemes, our proof relies on Gabber's theorem on the preservation of companionship.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-30T13:02:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F20",
      "14G15",
      "14A20",
      "14D22"
    ],
    "keywords": [
      "companions",
      "smooth schemes",
      "smooth artin stacks",
      "extend drinfelds theorem",
      "coarse moduli spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151208929Z"
    }
  }
}