{
  "annotation_id": "5c406ca4-a517-49b1-8771-5620aa3bec7d",
  "date_created": "2026-02-17T05:53:23.353000Z",
  "date_modified": "2026-02-17T05:53:23.353000Z",
  "file_hash": "00deffb239ad64e480f18f5f5b5594b0ebbb1afbc0b09622496ed6be586e3980",
  "private": false,
  "record": {
    "abstract": "This paper studies the structure of the Mordell--Weil groups of semiabelian varieties over algebraic extensions of number fields whose absolute Galois group is finitely generated, with particular emphasis on that generated by a single element. A probabilistic argument using the Haar measure on the absolute Galois group of a number field shows that almost all such fields are Kummer-faithful, i.e., the Mordell--Weil group of any semiabelian variety over any finite extension of such a field has trivial divisible part. This result implies that there exists a Kummer-faithful field algebraic over a number field whose absolute Galois group is abelian.",
    "arxiv_id": "2601.10298",
    "authors": [
      "Takuya Asayama"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Kummer-faithful fields with finitely generated absolute Galois group",
    "url": "https://arxiv.org/abs/2601.10298",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3bdd1a55-51fc-44ad-b913-27233c145612",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}