{
  "id": "2006.05803",
  "version": "v1",
  "published": "2020-06-10T12:41:05.000Z",
  "updated": "2020-06-10T12:41:05.000Z",
  "title": "Notes on the dual of the ideal class groups of CM-fields",
  "authors": [
    "Masato Kurihara"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, for a CM abelian extension $K/k$ of number fields, we propose a conjecture which describes completely the Fitting ideal of the minus part of the Pontryagin dual of the $T$-ray class group of $K$ for a set $T$ of primes as a ${\\rm Gal}(K/k)$-module. Here, we emphasize that we consider the full class group, and do not throw away the ramifying primes (namely, the object we study is not the quotient of the class group by the subgroup generated by the classes of ramifying primes). We prove that our conjecture is a consequence of the equivariant Tamagawa number conjecture, and also prove that the Iwasawa theoretic version of our conjecture holds true under the assumption $\\mu=0$ without assuming eTNC.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-10T12:41:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R23"
    ],
    "keywords": [
      "ideal class groups",
      "equivariant tamagawa number conjecture",
      "cm abelian extension",
      "ray class group",
      "iwasawa theoretic version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}