{
  "id": "math/0209370",
  "version": "v2",
  "published": "2002-09-26T14:48:14.000Z",
  "updated": "2004-01-07T17:19:21.000Z",
  "title": "Hodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification",
  "authors": [
    "J. I. Burgos",
    "J. Wildeshaus"
  ],
  "comment": "62 pages; the present version of the article is the slightly modified and final version of preprint no. math.AG/0209370. It will appear in Ann. scient. ENS",
  "journal": "Ann. Scient. Ec. Norm. Sup. 37 (2004), 363-413",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove an analogue for Hodge modules of Pink's theorem on the degeneration of l-adic sheaves (Math. Ann. 292). Let j be the open immersion of a Shimura variety M into its Baily-Borel compactification. Its boundary has a natural stratification into locally closed subsets, each of which is itself a Shimura variety (up to taking the quotient by the action of a finite group). Let i be the inclusion of an individual such stratum M'. Saito's formalism gives a functor i^* j_* from the bounded derived category of Hodge modules on M to that of Hodge modules on M'. Our result gives a formula for the effect of i^* j_* on automorphic Hodge modules, i.e., variations of Hodge structure coming from algebraic representations of the group associated to M. This formula is of a purely representation theoretical nature.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-01-07T17:19:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G35",
      "11F75",
      "14D07",
      "14F25",
      "14F40",
      "14F43",
      "32G20"
    ],
    "keywords": [
      "shimura variety",
      "higher direct images",
      "baily-borel compactification",
      "automorphic hodge modules",
      "natural stratification"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9370B"
    }
  }
}