{
  "id": "1710.09113",
  "version": "v1",
  "published": "2017-10-25T08:26:54.000Z",
  "updated": "2017-10-25T08:26:54.000Z",
  "title": "On a Noncommutative Iwasawa Main Conjecture for Function Fields",
  "authors": [
    "Malte Witte"
  ],
  "comment": "41 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We formulate and prove an analogue of the non-commutative Iwasawa Main Conjecture for $\\ell$-adic representations of the Galois group of a function field of characteristic $p$. We also prove a functional equation for the resulting non-commutative $L$-functions. As corollaries, we obtain non-commutative generalisations of the main conjecture for Picard-$1$-motives of Greither and Popescu and a main conjecture for abelian varieties over function fields in precise analogy to the $\\operatorname{GL}_2$ main conjecture of Coates, Fukaya, Kato, Sujatha and Venjakob.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-25T08:26:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11G20",
      "11S40",
      "11G10"
    ],
    "keywords": [
      "noncommutative iwasawa main conjecture",
      "function field",
      "non-commutative iwasawa main conjecture",
      "functional equation",
      "precise analogy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}