{
  "id": "2007.03060",
  "version": "v1",
  "published": "2020-07-06T20:55:57.000Z",
  "updated": "2020-07-06T20:55:57.000Z",
  "title": "Perverse sheaves and finite-dimensional algebras",
  "authors": [
    "Alessio Cipriani",
    "Jon Woolf"
  ],
  "comment": "11 pages",
  "categories": [
    "math.RT",
    "math.AT"
  ],
  "abstract": "Let $X$ be a topologically stratified space, $p$ be any perversity on $X$, and $k$ be a field. We show that the category of $p$-perverse sheaves on $X$, constructible with respect to the stratification and with coefficients in $k$, is equivalent to the category of finite-dimensional modules over a finite-dimensional algebra if and only if $X$ has finitely many strata and the same holds for the category of local systems on each of these. The main component in the proof is a construction of projective covers for simple perverse sheaves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-06T20:55:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G80",
      "55N33"
    ],
    "keywords": [
      "finite-dimensional algebra",
      "simple perverse sheaves",
      "finite-dimensional modules",
      "local systems",
      "main component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}