{
  "id": "2207.06353",
  "version": "v1",
  "published": "2022-07-13T17:04:52.000Z",
  "updated": "2022-07-13T17:04:52.000Z",
  "title": "Massey products in the étale cohomology of number fields",
  "authors": [
    "Eric Ahlqvist",
    "Magnus Carlson"
  ],
  "comment": "39 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We give formulas for 3-fold Massey products in the \\'etale cohomology of the ring of integers of a number field and use these to find the first known examples of imaginary quadratic fields with class group of $p$-rank two possessing an infinite $p$-class field tower, where $p$ is an odd prime. We also disprove McLeman's $(3,3)$-conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-13T17:04:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R34",
      "14F20",
      "14G25"
    ],
    "keywords": [
      "number field",
      "massey products",
      "class field tower",
      "imaginary quadratic fields",
      "disprove mclemans"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}