{
  "id": "math/0308165",
  "version": "v5",
  "published": "2003-08-18T15:29:27.000Z",
  "updated": "2007-03-17T02:29:59.000Z",
  "title": "Massey Products and Ideal Class Groups",
  "authors": [
    "Romyar Sharifi"
  ],
  "comment": "40 pages",
  "journal": "J. reine angew. Math. 603 (2007) 1-33",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider certain Massey products in the cohomology of a Galois extension of fields with coefficients in p-power roots of unity. We prove formulas for these products both in general and in the special case that the Galois extension in question is the maximal extension of a number field unramified outside a set of primes S including those above p and any archimedean places. We then consider those Z_p-Kummer extensions L of the maximal p-cyclotomic extension K of a number field that are unramified outside S. We show that Massey products describe the structure of a certain \"decomposition-free\" quotient of a graded piece of the maximal unramified abelian pro-p extension of L in which all primes above those in S split completely, with the grading arising from the augmentation filtration on the group ring of the Galois group of L/K. We explicitly describe examples of the maximal unramified abelian pro-p extensions of unramified outside p Kummer extensions of the cyclotomic field of all p-power roots of unity, for irregular primes p.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2007-03-17T02:29:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11R34",
      "11R29",
      "11R20",
      "12G05"
    ],
    "keywords": [
      "massey products",
      "ideal class groups",
      "maximal unramified abelian pro-p extension",
      "unramified outside",
      "number field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......8165S"
    }
  }
}