{
  "id": "math/0306403",
  "version": "v2",
  "published": "2003-06-27T20:49:36.000Z",
  "updated": "2003-07-19T15:10:23.000Z",
  "title": "On the Cohomology of Locally Symmetric Spaces and of their Compactifications",
  "authors": [
    "Leslie Saper"
  ],
  "comment": "71 pages, 30 figures, AMS-LaTeX, uses XyPic 3.7 package; to appear in the proceedings of the Harvard/M.I.T. conference \"Current Developments in Mathematics, 2002\", held in November 2002; minor errors fixed, added references, re-formatted to CDM style",
  "journal": "Current Developments in Mathematics, 2002 (D. Jerison, G. Lusztig, B. Mazur, T. Mrowka, W. Schmid, R. Stanley, and S.-T. Yau, eds.) International Press, 2003, pp. 219-289",
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "This expository article is an expanded version of talks given at the \"Current Developments in Mathematics, 2002\" conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the intersection cohomology of a real equal-rank Satake compactification of a locally symmetric space with that of the reductive Borel-Serre compactification. We motivate the conjecture with examples and then give an introduction to the various topics that are involved: intersection cohomology, the derived category, and compactifications of a locally symmetric space, particularly those above. We then give an overview of the theory of L-modules and micro-support (see math.RT/0112251) which was developed to solve the conjecture but has other important applications as well. We end with sketches of the proofs of three main theorems on L-modules that lead to the resolution of the conjecture. The text is enriched with many examples, illustrations, and references to the literature.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-07-19T15:10:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F75",
      "22E40",
      "32S60",
      "55N33",
      "14G35",
      "22E45"
    ],
    "keywords": [
      "locally symmetric space",
      "conjecture",
      "intersection cohomology",
      "real equal-rank satake compactification",
      "main theorems"
    ],
    "tags": [
      "conference paper",
      "research tool",
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 71,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6403S"
    }
  }
}