{
  "abstract": "For a finite group $G$, we define a constant spectral $G$-Mackey functor as a genuine $G$-spectrum in which the restrictions between categorical fixed points are equivalences. We further identify the full subcategory of constant spectral $G$-Mackey functors with the category of modules over a certain $\\mathbb{E}_1$-ring spectrum $R_G$. When $G=C_{p^n}$ is a cyclic $p$-group, we provide an explicit construction of the $\\mathbb{E}_1$-ring spectrum $R_{C_{p^n}}$. The proof uses a reconstruction theorem for genuine $C_{p^n}$-spectra, which might be of independent interest. As an application, we compute the $\\mathbb{Z}$-graded $C_{p^n}$-equivariant mod $p$ Steenrod algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05654",
  "author_total": 1,
  "authors": [
    {
      "name": "Kailin Pan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4jrk8bk8r7q02.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05654",
  "fulltext_url": null,
  "id": "4jrk8bk8r7q02",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05654",
  "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.AT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.05654",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4jrk8bk8r7q02.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05654",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05654"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Constant spectral Mackey functors and the equivariant Steenrod algebra",
  "title_text": "Constant spectral Mackey functors and the equivariant Steenrod algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4jrk8bk8r7q02",
  "venue": "arXiv",
  "versions": []
}