{
  "id": "1507.02370",
  "version": "v1",
  "published": "2015-07-09T04:40:35.000Z",
  "updated": "2015-07-09T04:40:35.000Z",
  "title": "A cohomological relation of unit groups over quadratic extensions of number fields",
  "authors": [
    "Derong Qiu"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $ G $ be a group of order $ 2, $ in this paper, we give a simple cohomological relation for finitely generated $ G-$modules, from which we provide new proofs for some known theorems about unit groups over quadratic extensions of number fields, as well as some new applications on Pell equations, units in CM number fields and class number of number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-09T04:40:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R11",
      "11R27",
      "11R29",
      "11R11",
      "11R27",
      "11R29"
    ],
    "keywords": [
      "unit groups",
      "quadratic extensions",
      "cm number fields",
      "class number",
      "simple cohomological relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150702370Q"
    }
  }
}