{
  "id": "math/0609410",
  "version": "v8",
  "published": "2006-09-14T15:45:55.000Z",
  "updated": "2009-10-19T08:22:20.000Z",
  "title": "Singular integers and p-class group of cyclotomic fields",
  "authors": [
    "Roland Queme"
  ],
  "comment": "The section 7 on the consequences of the previous sections of the article on the Vandiver's conjecture contains an error and is removed",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be an irregular prime. Let $K=\\Q(\\zeta)$ be the $p$-cyclotomic field. From Kummer and class field theory, there exist Galois extensions $S/\\Q$ of degree $p(p-1)$ such that $S/K$ is a cyclic unramified extension of degree $[S:K]=p$. We give an algebraic construction of the subfields $M$ of $S$ with degree $[M:\\Q]=p$ and an explicit formula for the prime decomposition and ramification of the prime number $p$ in the extensions $S/K$, $M/\\Q$ and $S/M$. In the last section, we examine the consequences of these results for the Vandiver's conjecture. This article is at elementary level on Classical Algebraic Number Theory.",
  "revisions": [
    {
      "version": "v8",
      "updated": "2009-10-19T08:22:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R18",
      "11R29",
      "11R32"
    ],
    "keywords": [
      "cyclotomic field",
      "singular integers",
      "p-class group",
      "classical algebraic number theory",
      "class field theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9410Q"
    }
  }
}