{
  "id": "1111.3718",
  "version": "v1",
  "published": "2011-11-16T06:59:23.000Z",
  "updated": "2011-11-16T06:59:23.000Z",
  "title": "Tensor functor from Smooth Motives to motives over a base",
  "authors": [
    "Anandam Banerjee"
  ],
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "Recently, Levine constructed a DG category whose homotopy category is equivalent to the full subcategory of motives over a base-scheme $S$ generated by the motives of smooth projective $S$-schemes, assuming that $S$ is itself smooth over a perfect field. In his construction, the tensor structure required $\\mathbb{Q}$-coefficients. The author has previously shown how to provide a tensor structure on the homotopy category mentioned above, when $S$ is semi-local and essentially smooth over a field of characteristic zero, extending Levine's tensor structure with $\\mathbb{Q}$-coefficients. In this article, it is shown that, under these conditions, the fully faithful functor $\\rho_S$ that Levine constructed from his category of smooth motives to the category $DM_S$ of motives over a base (defined by Cisinski-D\\'{e}glise) is a tensor functor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-16T06:59:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19E15",
      "18E30"
    ],
    "keywords": [
      "smooth motives",
      "tensor functor",
      "homotopy category",
      "extending levines tensor structure",
      "dg category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.3718B"
    }
  }
}