{
  "id": "1805.08902",
  "version": "v1",
  "published": "2018-05-22T23:11:14.000Z",
  "updated": "2018-05-22T23:11:14.000Z",
  "title": "On Picard groups of blocks of finite groups",
  "authors": [
    "Robert Boltje",
    "Radha Kessar",
    "Markus Linckelmann"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We show that the subgroup of the Picard group of a $p$-block of a finite group given by bimodules with endopermutation sources modulo the automorphism group of a source algebra is determined locally in terms of the fusion system on a defect group. We show that the Picard group of a block over the a complete discrete valuation ring ${\\mathcal O}$ of characteristic zero with an algebraic closure $k$ of ${\\mathbb F}_p$ as residue field is a colimit of finite Picard groups of blocks over $p$-adic subrings of ${\\mathcal O}$. We apply the results to blocks with an abelian defect group and Frobenius inertial quotient, and specialise this further to blocks with cyclic or Klein four defect groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-22T23:11:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20",
      "20C11"
    ],
    "keywords": [
      "finite group",
      "abelian defect group",
      "finite picard groups",
      "frobenius inertial quotient",
      "endopermutation sources modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}