{
  "id": "0804.3260",
  "version": "v1",
  "published": "2008-04-21T09:55:48.000Z",
  "updated": "2008-04-21T09:55:48.000Z",
  "title": "Milnor $K$-group attached to a torus and Birch-Tate conjecture",
  "authors": [
    "Takao Yamazaki"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT",
    "math.KT"
  ],
  "abstract": "We formulate (and prove under a certain assumption) a conjecture relating the order of Somekawa's Milnor $K$-group attached to a torus $T$ and the value of the Artin $L$-function attached to the cocharacter group of $T$ (regarded as an Artin representation) at $s=-1$. The case $T=\\G_m$ reduces to the classical Birch-Tate conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-21T09:55:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R70",
      "11R42",
      "19F15"
    ],
    "keywords": [
      "artin representation",
      "cocharacter group",
      "classical birch-tate conjecture",
      "somekawas milnor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.3260Y"
    }
  }
}