{
  "id": "2407.10502",
  "version": "v1",
  "published": "2024-07-15T07:48:13.000Z",
  "updated": "2024-07-15T07:48:13.000Z",
  "title": "Homology of strict polynomial functors over Fp-linear additive categories",
  "authors": [
    "Aurélien Djament",
    "Antoine Touzé"
  ],
  "comment": "This preprint reworks a part of the material of our previous preprint ''Functor homology over an additive category'' (hal-03432824 or arXiv:2111.09719), which is being completely reorganized. 48 pages",
  "categories": [
    "math.AT",
    "math.CT",
    "math.GR",
    "math.KT",
    "math.RT"
  ],
  "abstract": "We generalize the strong comparison theorem of Franjou, Friedlander, Scorichenko and Suslin to the setting of Fp-linear additive categories. Our results have a strong impact in terms of explicit computations of functor homology, and they open the way to new applications to stable homology of groups or to K-theory. As an illustration, we prove comparison theorems between cohomologies of classical algebraic groups over infinite perfect fields, in the spirit of a celebrated result of Cline, Parshall, Scott et van der Kallen for finite fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-15T07:48:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fp-linear additive categories",
      "strict polynomial functors",
      "strong comparison theorem",
      "van der kallen",
      "infinite perfect fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}