{
  "id": "0706.1498",
  "version": "v1",
  "published": "2007-06-11T15:54:50.000Z",
  "updated": "2007-06-11T15:54:50.000Z",
  "title": "On the derived category of 1-motives, I",
  "authors": [
    "Luca Barbieri-Viale",
    "Bruno Kahn"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We consider the category of Deligne 1-motives over a perfect field k of exponential characteristic p and its derived category for a suitable exact structure after inverting p. As a first result, we provide a fully faithful embedding into an etale version of Voevodsky's triangulated category of geometric motives. Our second main result is that this full embedding \"almost\" has a left adjoint, that we call \\LAlb. Applied to the motive of a variety we thus get a bounded complex of 1-motives, that we compute fully for smooth varieties and partly for singular varieties. As an application we give motivic proofs of Roitman type theorems (in characteristic 0).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-11T15:54:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived category",
      "roitman type theorems",
      "second main result",
      "etale version",
      "voevodskys triangulated category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.1498B"
    }
  }
}