{
  "abstract": "We study surjectivity of the geometric Sen map for perfectoid $G$-torsors over smooth rigid analytic spaces over $\\mathbb{C}_p$, where $G$ is a compact $p$-adic Lie group. We construct an affinoid perfectoid $\\mathbb{Z}_p^2$-torsor over a smooth curve whose Sen map is not surjective, thereby disproving Rodríguez Camargo's conjectured implication from perfectoidness to surjectivity. We prove that the Sen map of every perfectoid $G$-torsor over a smooth curve is nevertheless surjective on a Zariski open dense subset. Finally, we show that locally analytic decompletion implies Sen surjectivity for diamondian affinoid perfectoid torsors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08287",
  "author_total": 2,
  "authors": [
    {
      "name": "Tian Qiu"
    },
    {
      "name": "Jiahong Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d9yv3f58he0jx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08287",
  "fulltext_url": null,
  "id": "d9yv3f58he0jx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08287",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7211988491",
  "pdf_url": "https://arxiv.org/pdf/2609.08287",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d9yv3f58he0jx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.08287",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08287"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Surjectivity of the Geometric Sen Map of Perfectoid Torsors",
  "title_text": "On the Surjectivity of the Geometric Sen Map of Perfectoid Torsors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/d9yv3f58he0jx",
  "venue": "arXiv",
  "versions": []
}