{
  "id": "math/0605603",
  "version": "v2",
  "published": "2006-05-23T02:10:50.000Z",
  "updated": "2006-06-16T10:34:51.000Z",
  "title": "Weight filtration on the cohomology of algebraic varieties",
  "authors": [
    "Masaki Hanamura",
    "Morihiko Saito"
  ],
  "comment": "11 pages, title is changed",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that the etale cohomology (with compact supports) of an algebraic variety $X$ over an algebraically closed field has the canonical weight filtration $W$, and prove that the middle weight part of the cohomology with compact supports of $X$ is a subspace of the intersection cohomology of a compactification $X'$ of X, or equivalently, the middle weight part of the (so-called) Borel-Moore homology of $X$ is a quotient of the intersection cohomology of $X'$. We are informed that this has been shown by A. Weber in the case $X$ is proper (and $k=\\bC$) using a theorem of G. Barthel, J.-P. Brasselet, K.-H. Fieseler, O. Gabber and L. Kaup on morphisms between intersection complexes. We show that the assertion immediately follows from Gabber's purity theorem for intersection complexes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-06-16T10:34:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F43"
    ],
    "keywords": [
      "algebraic variety",
      "middle weight part",
      "compact supports",
      "intersection complexes",
      "intersection cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5603H"
    }
  }
}