{
  "id": "2012.03982",
  "version": "v1",
  "published": "2020-12-07T19:00:26.000Z",
  "updated": "2020-12-07T19:00:26.000Z",
  "title": "Equivariant sheaves for profinite groups",
  "authors": [
    "David Barnes",
    "Danny Sugrue"
  ],
  "comment": "36 pages",
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "We develop the theory of equivariant sheaves over profinite spaces, where the group is also taken to be profinite. We construct a good notion of equivariant presheaves, with a suitable sheafification functor. Using these results on equivariant presheaves, we give explicit constructions of products of equivariant sheaves of R-modules. We introduce an equivariant analogue of skyscraper sheaves, which allows us to show that the category of equivariant sheaves of R-modules over a profinite space has enough injectives. This paper also provides the basic theory for results by the authors on giving an algebraic model for rational G-spectra in terms of equivariant sheaves over profinite spaces. For those results, we need a notion of Weyl-G-sheaves over the space of closed subgroups of G. We show that Weyl-G-sheaves of R-modules form an abelian category, with enough injectives, that is a full subcategory of equivariant sheaves of R-modules. Moreover, we show that the inclusion functor has a right adjoint.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-07T19:00:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B40",
      "18F20",
      "20E18"
    ],
    "keywords": [
      "equivariant sheaves",
      "profinite groups",
      "profinite space",
      "equivariant presheaves",
      "right adjoint"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}