{
  "id": "math/0208027",
  "version": "v6",
  "published": "2002-08-04T21:35:17.000Z",
  "updated": "2005-11-03T03:01:57.000Z",
  "title": "Finiteness of rigid cohomology with coefficients",
  "authors": [
    "Kiran S. Kedlaya"
  ],
  "comment": "70 pages; v6: corrections to 8.3, 8.4, 9.3",
  "journal": "preprint; published version: Duke Math. J. 134 (2006), 15-97",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We prove that for any field k of characteristic p>0, any separated scheme X of finite type over k, and any overconvergent F-isocrystal E over X, the rigid cohomology H^i(X, E) and rigid cohomology with compact supports H^i_c(X,E) are finite dimensional vector spaces. We also establish Poincare duality and the Kunneth formula with coefficients. The arguments use a pushforward construction in relative dimension 1, based on a relative version of Crew's conjecture on the quasi-unipotence of certain p-adic differential equations.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2005-11-03T03:01:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F30",
      "14F40",
      "14G22"
    ],
    "keywords": [
      "rigid cohomology",
      "coefficients",
      "finiteness",
      "finite dimensional vector spaces",
      "p-adic differential equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 70,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......8027K"
    }
  }
}