{
  "abstract": "We prove a rigidity theorem for $π_*$-étale $\\mathbb E_k$-algebras over an $\\mathbb E_{k+1}$-ring spectrum: the category of $π_*$-étale extensions of an $\\mathbb E_k$-algebra is identified with the ordinary category of étale Dirac algebras over its graded homotopy Dirac ring. The proof develops a relative Goerss-Hopkins type obstruction theory in synthetic spectra, including an $I$-complete version. As an application, the completed obstruction theory constructs the $I_n$-complete $\\mathbb E_3$-$MU_{(p)}$-algebra realization of the Lubin-Tate theory, hence an $\\mathbb E_4$-orientation $MU_{(p)}\\to E_n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22680",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiansheng Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bvg70qfg3367e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22680",
  "fulltext_url": null,
  "id": "bvg70qfg3367e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22680",
  "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",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7171568138",
  "pdf_url": "https://arxiv.org/pdf/2607.22680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bvg70qfg3367e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2607.22680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A rigidity theorem for $π_*$-étale $\\mathbb E_k$-algebras",
  "title_text": "A rigidity theorem for π_*-étale 𝔼_k-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/bvg70qfg3367e",
  "venue": "arXiv",
  "versions": []
}