{
  "id": "2407.15667",
  "version": "v1",
  "published": "2024-07-22T14:29:07.000Z",
  "updated": "2024-07-22T14:29:07.000Z",
  "title": "On even $K$-groups over $p$-adic Lie extensions of global function fields",
  "authors": [
    "Meng Fai Lim"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be a fixed prime number, and $F$ a global function field of characteristic not equal to $p$. In this paper, we shall study the growth of the Sylow $p$-subgroups of the even $K$-groups in a $p$-adic Lie extension of $F$, where the $p$-adic Lie extension is assumed to contain the cyclotomic $\\mathbb{Z}_p$-extension of $F$. We also establish a duality between the direct limit and inverse limit of the even $K$-groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-22T14:29:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adic lie extension",
      "global function field",
      "fixed prime number",
      "direct limit",
      "inverse limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}