{
  "id": "math/0509448",
  "version": "v2",
  "published": "2005-09-20T10:06:40.000Z",
  "updated": "2009-01-26T18:24:06.000Z",
  "title": "Sur la compatibilité à Frobenius de l'isomorphisme de dualité relative",
  "authors": [
    "Daniel Caro"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $\\V$ be a mixed characteristic complete discrete valuation ring, let $\\X$ and $\\Y$ be two smooth formal $\\V$-schemes, let $f_0$ : $X \\to Y$ be a projective morphism between their special fibers, let $T$ be a divisor of $Y$ such that $T_X := f_0 ^{-1} (T) $ is a divisor of $X$ and let $\\M \\in D ^\\mathrm{b}_\\mathrm{coh} (\\D ^\\dag_{\\X} (\\hdag T_X)_{\\Q})$. We construct the relative duality isomorphism $ f_{0T +} \\circ \\DD_{\\X, T_X} (\\M) \\riso \\DD_{\\Y, T} \\circ f_{0T +} (\\M)$. This generalizes the known case when there exists a lifting $f : \\X \\to \\Y$ of $f_{0}$. Moreover, when $f_0$ is a closed immersion, we prove that this isomorphism commutes with Frobenius.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-26T18:24:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F10",
      "14F30"
    ],
    "keywords": [
      "mixed characteristic complete discrete valuation",
      "lisomorphisme",
      "characteristic complete discrete valuation ring",
      "smooth formal",
      "special fibers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9448C"
    }
  }
}