{
  "id": "0902.4856",
  "version": "v2",
  "published": "2009-02-27T15:39:57.000Z",
  "updated": "2009-07-28T11:44:45.000Z",
  "title": "Resolutions for representations of reductive p-adic groups via their buildings",
  "authors": [
    "Ralf Meyer",
    "Maarten Solleveld"
  ],
  "comment": "second version, some minor corrections",
  "journal": "J. Reine Angew. Math. 647 (2010), 115-150",
  "doi": "10.1515/CRELLE.2010.075",
  "categories": [
    "math.RT"
  ],
  "abstract": "Schneider-Stuhler and Vigneras have used cosheaves on the affine Bruhat-Tits building to construct natural finite type projective resolutions for admissible representations of reductive p-adic groups in characteristic not equal to p. We use a system of idempotent endomorphisms of a representation with certain properties to construct a cosheaf and a sheaf on the building. We establish that these are acyclic and compute homology and cohomology with these coefficients. This implies Bernstein's result that certain subcategories of the category of representations are Serre subcategories. Furthermore, we also get results for convex subcomplexes of the building. Following work of Korman, this leads to trace formulas for admissible representations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-28T11:44:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G25",
      "51E24",
      "20E42"
    ],
    "keywords": [
      "reductive p-adic groups",
      "natural finite type projective resolutions",
      "construct natural finite type projective",
      "admissible representations",
      "implies bernsteins result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.4856M"
    }
  }
}