{
  "abstract": "Let $X=(|X|,\\mathcal O_X)$ be a derived smooth manifold in the sense of Spivak. After passing from the simplicial $C^\\infty$-structure sheaf to a connective spectral structure sheaf $\\mathbb O_X$, we construct the intrinsic Picard hypersheaf of invertible $\\mathbb O_X$-modules and define its delooping \\[ \\operatorname{Br}^{\\mathrm{Pic}}_X :=B\\operatorname{Pic}_{\\mathbb O_X}. \\] On the ordinary open site of $|X|$, we prove an equivalence of hypersheaves of connected pointed spaces \\[ \\operatorname{Br}^{\\mathrm{Pic}}_X \\simeq K(\\underline{\\mathbb Z},1) \\times B^2\\operatorname{GL}_1(\\mathbb O_X). \\] The statement is unconditional at the level of Picard torsors. Its interpretation as a classification of forms of the module category is made under an explicit category-valued open-hyperdescent hypothesis, and representability by an internal $E_1$-algebra is separated further by a global compact-local-generator hypothesis together with internal mapping objects, their base-change equivalences, and relative Morita continuity. For an ordinary paracompact smooth manifold $M$, the real and complex coefficient theories recover, respectively, the pointed-set decompositions \\[ H^1_{\\mathrm{sing}}(M;\\mathbb Z) \\times H^2_{\\mathrm{sing}}(M;\\mathbb Z/2) \\quad\\text{and}\\quad H^1_{\\mathrm{sing}}(M;\\mathbb Z) \\times H^3_{\\mathrm{sing}}(M;\\mathbb Z). \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22668",
  "author_total": 2,
  "authors": [
    {
      "name": "Yimu Mao"
    },
    {
      "name": "Christopher Tropp"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4cpz1zfr2t1nd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22668",
  "fulltext_url": null,
  "id": "4cpz1zfr2t1nd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22668",
  "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.GM"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7171557352",
  "pdf_url": "https://arxiv.org/pdf/2607.22668",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4cpz1zfr2t1nd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2607.22668",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22668"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Homotopy and Cohomology in Algebraic Topology",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A Picard-Theoretic Brauer Object for Derived Smooth Manifolds",
  "title_text": "A Picard-Theoretic Brauer Object for Derived Smooth Manifolds",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/4cpz1zfr2t1nd",
  "venue": "arXiv",
  "versions": []
}