{
  "id": "math/0603203",
  "version": "v1",
  "published": "2006-03-09T00:01:43.000Z",
  "updated": "2006-03-09T00:01:43.000Z",
  "title": "Some relations between the topological and geometric filtration for smooth projective varieties",
  "authors": [
    "Wenchuan Hu"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In the first part of this paper, we show that the assertion \"T_pH_k(X,Q)=G_pH_k(X,Q)\" (which is called the Friedlander-Mazur conjecture) is a birationally invariant statement for smooth projective varieties X when p=dim(X)-2 and when p=1. We also establish the Friedlander-Mazur conjecture in certain dimensions. More precisely, for a smooth projective variety X, we show that the topological filtration T_pH_{2p+1}(X,Q) coincides with the geometric filtration G_pH_{2p+1}(X,Q) for all p. (Friedlander and Mazur had previously shown that T_pH_{2p}(X,Q})=G_pH_{2p}(X,Q)). As a corollary, we conclude that for a smooth projective threefold X, T_pH_k(X,Q)=G_pH_k(X,Q) for all k\\geq 2p\\geq 0 except for the case p=1,k=4. Finally, we show that the topological and geometric filtrations always coincide if Suslin's conjecture holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-09T00:01:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25",
      "14F43"
    ],
    "keywords": [
      "smooth projective variety",
      "geometric filtration",
      "friedlander-mazur conjecture",
      "topological",
      "suslins conjecture holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3203H"
    }
  }
}