{
  "id": "2207.13408",
  "version": "v1",
  "published": "2022-07-27T09:45:36.000Z",
  "updated": "2022-07-27T09:45:36.000Z",
  "title": "The Segal conjecture for smash powers",
  "authors": [
    "Håkon Schad Bergsaker",
    "John Rognes"
  ],
  "comment": "Dedicated to our PhD advisor and grand-advisor Gunnar Carlsson, on the occasion of his 70th birthday",
  "categories": [
    "math.AT"
  ],
  "abstract": "We prove that the comparison map from $G$-fixed points to $G$-homotopy fixed points, for the $G$-fold smash power of a bounded below spectrum $B$, becomes an equivalence after $p$-completion if $G$ is a finite $p$-group and $H_*(B; F_p)$ is of finite type. We also prove that the map becomes an equivalence after $I(G)$-completion if $G$ is any finite group and $\\pi_*(B)$ is of finite type, where $I(G)$ is the augmentation ideal in the Burnside ring.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-27T09:45:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P91",
      "55P42"
    ],
    "keywords": [
      "segal conjecture",
      "finite type",
      "fold smash power",
      "completion",
      "augmentation ideal"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}