{
  "id": "1707.07398",
  "version": "v1",
  "published": "2017-07-24T04:21:11.000Z",
  "updated": "2017-07-24T04:21:11.000Z",
  "title": "Reciprocity sheaves and motives with modulus",
  "authors": [
    "Bruno Kahn",
    "Shuji Saito",
    "Takao Yamazaki"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We exhibit an intimate relationship between \"motives with modulus\" from arXiv:1511.07124 [math.AG] and \"reciprocity sheaves\" from arXiv:1402.4201 [math.AG]. Assuming resolution of singularities, we prove that the triangulated category of effective motivic complexes $\\mathbf{MDM}^{\\mathrm{eff}}$ admits a $t$-structure whose heart is equivalent to the category of reciprocity Nisnevich sheaves. We also give an isomorphism between some Hom groups in $\\mathbf{MDM}^{\\mathrm{eff}}$ and the hypercohomology of some Suslin complexes with modulus. As an application, we prove some Mayer-Vietoris sequences for Suslin homology with modulus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-24T04:21:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19E15",
      "14F42",
      "19D45",
      "19F15"
    ],
    "keywords": [
      "reciprocity sheaves",
      "reciprocity nisnevich sheaves",
      "effective motivic complexes",
      "suslin homology",
      "intimate relationship"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}