{
  "id": "math/0605125",
  "version": "v5",
  "published": "2006-05-04T14:50:12.000Z",
  "updated": "2012-11-26T13:25:27.000Z",
  "title": "On the stability by tensor products of complexes of arithmetic D-modules",
  "authors": [
    "Daniel Caro"
  ],
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let $V$ be a complete discrete valued ring of mixed characteristic $(0,p)$, $K$ its field of fractions, $k$ its residue field which is supposed to be perfect. Let $X$ be a separated $k$-scheme of finite type and $Y$ be a smooth open of $X$. We check that the equivalence of categories $sp_{(Y,X),+}$ (from the category of overconvergent isocrystals on $(Y,X)/K$ to that of overcoherent isocrystals on $(Y,X)/K$) commutes with tensor products. Next, in Berthelot's theory of arithmetic $\\mathcal{D}$-modules, we prove the stability under tensor products of the devissability in overconvergent isocrystals. With Frobenius structures, we get the stability under tensor products of the overholonomicity.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-11-26T13:25:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F30",
      "14F10"
    ],
    "keywords": [
      "tensor products",
      "arithmetic d-modules",
      "overconvergent isocrystals",
      "berthelots theory",
      "overcoherent isocrystals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5125C"
    }
  }
}