{
  "abstract": "We prove that given an analytic supermanifold $X$ over a complete field on which the additive supergroup $\\mathbb{A}^{0|n}$ of super-dimension $0|n$ acts freely (in an appropriate sense), the quotient $X/\\mathbb{A}^{0|n}$ exists as an analytic supermanifold, and the canonical morphism $X \\to X/\\mathbb{A}^{0|n}$ is an $\\mathbb{A}^{0|n}$-principal bundle. A stronger version of this result is proven for $C^{\\infty}$-supermanifolds, whereby $X \\to X/\\mathbb{A}^{0|n}$ is a trivial $\\mathbb{A}^{0|n}$-principal bundle. Previously, Polishchuk [18] established an algebro-geometric analogue, which proves that a superscheme $X$ with free $\\mathbb{A}^{0|n}$-action gives rise to a locally trivial $\\mathbb{A}^{0|n}$-torsor $X \\to X/\\mathbb{A}^{0|n}$. This result is proven here in an alternative, elementary way. To all of these, a Hopf-algebraic approach is effectively employed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25564",
  "author_total": 2,
  "authors": [
    {
      "name": "Akira Masuoka"
    },
    {
      "name": "Takuya Oe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0775pnssha63b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25564",
  "fulltext_url": null,
  "id": "0775pnssha63b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25564",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7223025154",
  "pdf_url": "https://arxiv.org/pdf/2610.25564",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0775pnssha63b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25564",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25564"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Superschemes and supermanifolds with free $\\mathbb{A}^{0|n}$-action",
  "title_text": "Superschemes and supermanifolds with free 𝔸^0|n-action",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/0775pnssha63b",
  "venue": "arXiv",
  "versions": []
}