{
  "id": "2210.00168",
  "version": "v1",
  "published": "2022-10-01T02:22:29.000Z",
  "updated": "2022-10-01T02:22:29.000Z",
  "title": "On the structure of even $K$-groups of rings of algebraic integers",
  "authors": [
    "Meng Fai Lim"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we describe the higher even $K$-groups of the ring of integers of a number field in terms of class groups of an appropriate extension of the number field in question. This is a natural extension of the previous collective works of Browkin, Keune and Kolster, where they considered the case of $K_2$. We then revisit the Kummer's criterion of totally real fields as generalized by Greenberg and Kida. In particular, we give an algebraic $K$-theoretical formulation of this criterion which we will prove using the algebraic $K$-theoretical results developed here.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-01T02:22:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic integers",
      "number field",
      "appropriate extension",
      "natural extension",
      "kummers criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}