{
  "id": "2212.03187",
  "version": "v1",
  "published": "2022-12-06T18:02:43.000Z",
  "updated": "2022-12-06T18:02:43.000Z",
  "title": "Homological growth of Artin kernels in positive characteristic",
  "authors": [
    "Sam P. Fisher",
    "Sam Hughes",
    "Ian J. Leary"
  ],
  "comment": "21 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove an analogue of the L\\\"uck Approximation Theorem in positive characteristic for certain residually finite rationally soluble groups including right-angled Artin groups and Bestvina--Brady groups. Specifically, we prove that the mod $p$ homology growth equals the dimension of the group homology with coefficients in a certain universal division ring and this is independent of the choice of residual chain. We also consider a number of applications to fibring, amenable category, and minimal volume entropy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-06T18:02:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20J05",
      "16K99",
      "16S35",
      "20E26",
      "20F36",
      "20F65",
      "57M07"
    ],
    "keywords": [
      "positive characteristic",
      "artin kernels",
      "homological growth",
      "finite rationally soluble groups",
      "minimal volume entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}