{
  "id": "2011.08776",
  "version": "v1",
  "published": "2020-11-17T17:03:16.000Z",
  "updated": "2020-11-17T17:03:16.000Z",
  "title": "Annihilators of the ideal class group of a cyclic extension of a global function field",
  "authors": [
    "Pascal Stucky"
  ],
  "comment": "31 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be a global function field and fix a place $\\infty$ of $K$. Let $L/K$ be a finite real abelian extension, i.e. a finite, abelian extension such that $\\infty$ splits completely in $L$. Then we define a group of elliptic units $C_L$ in $\\mathcal{O}_L^\\times$ analogously to Sinnott's cyclotomic units and compute the index $[\\mathcal{O}_L^\\times:C_L]$. In the second part of this article, we additionally assume that $L$ is a cyclic extension of prime power degree. Then we can use the methods from Greither and Ku\\v{c}era to take certain roots of these elliptic units and prove a result on the annihilation of the $p$-part of the class group of $L$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-17T17:03:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R20",
      "11R58",
      "11R27",
      "11G09"
    ],
    "keywords": [
      "global function field",
      "ideal class group",
      "cyclic extension",
      "annihilators",
      "finite real abelian extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}