{
  "abstract": "We prove a projection formula for homotopy fixed points of trivial actions of finite $p$-groups. More precisely, for every bounded-below, $p$-complete spectrum $X$ whose mod-$p$ homology is $I$-complete, the canonical map \\[ (\\mathbb S_p)^{BG}\\otimes X \\overset{\\simeq}{\\rightarrow} X^{BG} \\] is an equivalence for every finite $p$-group $G$, where $I$ is the augmentation ideal of the Steenrod algebra. Building on earlier joint work with Burklund, our proof combines the Adams--Gunawardena--Miller calculation with an adaptation of Carlsson's induction. As an application, using the work of Yuan, we construct height-one semiadditive lifts of such spectra and show that their cohomology of $p$-finite spaces depends only on the $1$-type.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40209",
  "author_total": 1,
  "authors": [
    {
      "name": "Vignesh Subramanian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f4tbdtkvxh1cp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40209",
  "fulltext_url": null,
  "id": "f4tbdtkvxh1cp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40209",
  "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/2610.40209",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f4tbdtkvxh1cp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40209",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40209"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Segal conjecture for large objects and semiadditive lifts",
  "title_text": "The Segal conjecture for large objects and semiadditive lifts",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/f4tbdtkvxh1cp",
  "venue": "arXiv",
  "versions": []
}