{
  "id": "2011.11859",
  "version": "v1",
  "published": "2020-11-22T07:54:46.000Z",
  "updated": "2020-11-22T07:54:46.000Z",
  "title": "Motives with modulus, III: The categories of motives",
  "authors": [
    "Bruno Kahn",
    "Hiroyasu Miyazaki",
    "Shuji Saito",
    "Takao Yamazaki"
  ],
  "comment": "60 pages. arXiv admin note: text overlap with arXiv:1511.07124",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "We construct and study a triangulated category of motives with modulus $\\mathbf{MDM}_{\\mathrm{gm}}^{\\mathrm{eff}}$ over a field $k$ that extends Voevodsky's category $\\mathbf{DM}_{\\mathrm{gm}}^{\\mathrm{eff}}$ in such a way as to encompass non-homotopy invariant phenomena. In a similar way as $\\mathbf{DM}_{\\mathrm{gm}}^{\\mathrm{eff}}$ is constructed out of smooth $k$-varieties, $\\mathbf{MDM}_{\\mathrm{gm}}^{\\mathrm{eff}}$ is constructed out of proper modulus pairs, introduced in Part I of this work. To such a modulus pair we associate its motive in $\\mathbf{MDM}_{\\mathrm{gm}}^{\\mathrm{eff}}$. In some cases the $\\mathrm{Hom}$ group in $\\mathbf{MDM}_{\\mathrm{gm}}^{\\mathrm{eff}}$ between the motives of two modulus pairs can be described in terms of Bloch's higher Chow groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-22T07:54:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19E15",
      "14F42",
      "19D45",
      "19F15"
    ],
    "keywords": [
      "blochs higher chow groups",
      "encompass non-homotopy invariant phenomena",
      "proper modulus pairs",
      "extends voevodskys category",
      "similar way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 60,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}