{
  "abstract": "We propose a of definition conjugate stack for a class of suitable $\\mathbb{E}_3$-$\\mathrm{MU}$-algebras that includes the truncated Brown-Peterson spectra $\\mathrm{BP}\\langle n \\rangle$ for all heights $n$. Then we calculate part of $\\mathrm{BP}\\langle n \\rangle^{\\mathrm{conj}}$ as a quotient stack in terms of Witt vectors. To perform this computation we study generalized Thom spectra and their relative Topological Hochschild Homology. We exhibit the Eilenberg-Mac Lane spectrum $\\mathrm{H}\\mathbb{F}_2$ as a $\\mathbb{E}_3$-$\\mathrm{MU}$-Thom spectrum, the $p$-local Eilenberg-Mac Lane spectra $\\mathrm{H}\\mathbb{Z}/p^n$ (except for $\\mathrm{H}\\mathbb{Z}/4$) and $\\mathrm{H}\\mathbb{Z}_{(p)}$ as $\\mathbb{E}_3$-$\\mathrm{MU}_{(p)}$-Thom spectra, and the connective complex K-theory spectrum $ku$ as $\\mathbb{E}_1$-$\\mathrm{MU}$-Thom spectra. We accompany these ``go\" results with ``no-go\" results that show these ``go\" results do not admit $\\mathbb{E}_{\\infty}$-refinements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18754",
  "author_total": 1,
  "authors": [
    {
      "name": "Preston Cranford"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16chcqaq327hh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18754",
  "fulltext_url": null,
  "id": "16chcqaq327hh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18754",
  "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.AT"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7221823202",
  "pdf_url": "https://arxiv.org/pdf/2610.18754",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16chcqaq327hh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18754",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18754"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Generalized Thom Spectra, Conjugate Stacks, and truncated Brown-Peterson Spectra",
  "title_text": "Generalized Thom Spectra, Conjugate Stacks, and truncated Brown-Peterson Spectra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/16chcqaq327hh",
  "venue": "arXiv",
  "versions": []
}