{
  "id": "1307.3175",
  "version": "v6",
  "published": "2013-07-11T16:36:15.000Z",
  "updated": "2016-05-29T13:52:33.000Z",
  "title": "Mixed motives and quotient stacks: Abelian varieties",
  "authors": [
    "Isamu Iwanari"
  ],
  "comment": "a new version",
  "categories": [
    "math.AG",
    "math.AT",
    "math.NT"
  ],
  "abstract": "We prove that the symmetric monoidal category of mixed motives generated by an abelian variety (more generally, an abelian scheme) can be described as a certain module category. More precisely, we describe it as the category of quasi-coherent complexes over a derived quotient stack constructed from a motivic algebra of the abelian variety. We then study the structure of the motivic Galois groups of their mixed motives. We prove that the motivic Galois group is decomposed into a unipotent part constructed from the motivic algebra, and the reductive quotient which is the Tannaka dual of Grothendieck numerical motives.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-12-20T13:06:52.000Z",
      "comment": "simplified arguments and fixed errors in section 4",
      "journal": null,
      "doi": null
    },
    {
      "version": "v6",
      "updated": "2016-05-29T13:52:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian variety",
      "mixed motives",
      "motivic galois group",
      "motivic algebra",
      "symmetric monoidal category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.3175I"
    }
  }
}