{
  "id": "2010.10372",
  "version": "v1",
  "published": "2020-10-20T15:26:51.000Z",
  "updated": "2020-10-20T15:26:51.000Z",
  "title": "On sheaves in finite group representations",
  "authors": [
    "Tengfei Xiong",
    "Fei Xu"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Given a general finite group $G$, we consider several categories built on it, their Grothendieck topologies and resulting sheaf categories. We give an intrinsic new proof to the equivalence of M. Artin between the category of sheaves on the orbit category and that of group representations. We also show that the category of group representations is embedded into a sheaf category on the transporter category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-20T15:26:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C05",
      "18F10",
      "18A25",
      "18F20"
    ],
    "keywords": [
      "finite group representations",
      "sheaf category",
      "general finite group",
      "orbit category",
      "grothendieck topologies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}