{
  "annotation_id": "dd1d5a81-d1bf-40f9-b60a-f87c9d884a12",
  "date_created": "2026-02-17T05:53:08.766000Z",
  "date_modified": "2026-02-17T05:53:08.766000Z",
  "file_hash": "f569444b1a5bccec0694c39c2bc03f5f4b422aa9bd4bf624d225cc3f54ed156c",
  "private": false,
  "record": {
    "abstract": "In this paper we are interested in the stability of the $2$-rank of the class group in the cyclotomic $\\mathbb{Z}_2$-extension of real biquadratic fields. In fact, we give several families of real biquadratic fields $K$ such that $ rank(A(K)) =rank(A_\\infty(K))$ and $rank(A(K))\\leq 3$, where $A(K)$ and $A_\\infty(K)$ are the $2$-class group and the $2$-Iwasawa module of $K$ respectively. Moreover, Greenberg\u0027s conjecture is verified for some new families of number fields; in particular, we determine the complete list of all real biquadratic fields with trivial $2$-Iwasawa module. This work is a continuation of M. M. Chems-Eddin, Greenberg\u0027s conjecture and Iwasawa module of real biquadratic fields I, J. Number Theory, 281 (2026), 224-266.",
    "arxiv_id": "2601.07067",
    "authors": [
      "Mohamed Mahmoud Chems-Eddin",
      "Hamza El Mamry"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Greenberg\u0027s conjecture and Iwasawa module of Real biquadratic fields II",
    "url": "https://arxiv.org/abs/2601.07067",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "934a8de2-423b-4cdf-bf1d-db56535c2b5a",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}