{
  "annotation_id": "d22bd9fd-afa1-4aae-a875-41028640d40c",
  "date_created": "2026-02-17T05:53:11.280000Z",
  "date_modified": "2026-02-17T05:53:11.280000Z",
  "file_hash": "b7d8d1d1e2f2240bfb5428c1937e3b3483480f27c9192bb03d769810f63148d7",
  "private": false,
  "record": {
    "abstract": "Anabelian geometry suggests that, for suitably geometric objects, their \\\u0027etale fundamental group determines the object up to isomorphism. From a group-theoretic viewpoint, this philosophy requires rigidity properties of the associated \\\u0027etale fundamental groups, which often follow from their center-freeness. In fact, some profinite groups arising from anabelian geometry are center-free. In the present paper, we investigate how such center-freeness behaves when passing to maximal $m$-step solvable quotients for any integer $m\\geq 2$. In particular, we show that the maximal $m$-step solvable quotient of the geometric \\\u0027etale fundamental group of a hyperbolic curve over a field of characteristic $0$ is center-free. Furthermore, we show that this implies the injectivity statement, i.e., the rigidity property, of the $m$-step solvable Grothendieck conjecture.",
    "arxiv_id": "2601.07112",
    "authors": [
      "Naganori Yamaguchi"
    ],
    "categories": [
      "math.GR",
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Center-freeness of finite-step solvable groups arising from anabelian geometry",
    "url": "https://arxiv.org/abs/2601.07112",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fe60baca-1bc9-44aa-9ad1-462f31643524",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}