{
  "id": "math/0112250",
  "version": "v4",
  "published": "2001-12-22T03:03:37.000Z",
  "updated": "2005-05-13T18:02:28.000Z",
  "title": "L-modules and the Conjecture of Rapoport and Goresky-MacPherson",
  "authors": [
    "Leslie Saper"
  ],
  "comment": "16 pages, 4 figures, AMS-LaTeX, smfart.cls, uses xypic 3.7 package; v2: minor typos fixed, definitions of D_P(V) and n_P(V) corrected; v3: various references added in footnotes; v4: updated bibliography, revised and translated abstract, minor typos fixed",
  "journal": "Formes Automorphes (I) -- Actes du Semestre du Centre \\'Emile Borel, printemps 2000 (J. Tilouine, H. Carayol, M. Harris, and M.-F. Vign\\'eras, eds.), Ast\\'erisque 298 (2005), pp. 319-334",
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "Consider the middle perversity intersection cohomology groups of various compactifications of a Hermitian locally symmetric space. Rapoport and independently Goresky and MacPherson have conjectured that these groups coincide for the reductive Borel-Serre compactification and the Baily-Borel-Satake compactification. This paper describes the theory of L-modules and how it is used to solve the conjecture. More generally we consider a Satake compactification for which all real boundary components are equal-rank. Details will be given elsewhere (math.RT/0112251). As another application of L-modules, we prove a vanishing theorem for the ordinary cohomology of a locally symmetric space. This answers a question raised by Tilouine.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2005-05-13T18:02:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F75",
      "22E40",
      "32S60",
      "55N33",
      "14G35",
      "22E45"
    ],
    "keywords": [
      "conjecture",
      "middle perversity intersection cohomology groups",
      "goresky-macpherson",
      "compactification",
      "real boundary components"
    ],
    "tags": [
      "research tool",
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....12250S"
    }
  }
}