{
  "id": "math/0501548",
  "version": "v2",
  "published": "2005-01-31T10:39:38.000Z",
  "updated": "2005-06-02T12:02:55.000Z",
  "title": "Homological algebra for Schwartz algebras of reductive p-adic groups",
  "authors": [
    "Ralf Meyer"
  ],
  "comment": "34 pages, version 2 contains, in addition, a discussion about formal dimensions from the point of view of Schwartz algebras and von Neumann algebras",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let G be a reductive group over a non-Archimedean local field. Then the canonical functor from the derived category of smooth tempered representations of G to the derived category of all smooth representations of G is fully faithful. Here we consider representations on bornological vector spaces. As a consequence, if V and W are two tempered irreducible representations and if V or W is square-integrable, then Ext_G^n(V,W) vanishes for all n>0. We use this to prove in full generality a formula for the formal dimension of square-integrable representations due to Schneider and Stuhler.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-06-02T12:02:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "18E30"
    ],
    "keywords": [
      "reductive p-adic groups",
      "schwartz algebras",
      "homological algebra",
      "non-archimedean local field",
      "derived category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1548M"
    }
  }
}