{
  "abstract": "We compute the first two k-invariants of the Picard spectra of KU and KO by analyzing their Picard groupoids and constructing their unit spectra as global sections of sheaves on the category of manifolds.This allows us to determine the E 1 -structures of their truncations Pic.KU/Œ0; 3 and Pic.KO/Œ0; 2. It follows that these truncated Picard spaces represent the Brauer groups of Z=2-graded algebra bundles of Donovan, Karoubi, Moutuou and Maycock; the Brauer groups of super 2-lines; and the K-theory twists of Freed, Hopkins and Teleman.Our results also imply that these spaces represent twists of Stringand Spin-structures on manifolds and can be used to twist tmf-cohomology.Finally, we are able to identify pic.KU/Œ0; 3 with a cotruncation of the Anderson dual of the sphere spectrum.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics and Statistics, University of Nevada, Reno, Reno, NV, United States",
    "Department of Mathematics, University of Illinois Urbana-Champaign, Urbana, IL, United States",
    "Department of Mathematics, The Johns Hopkins University, Baltimore, MD, United States"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jonathan Beardsley"
    },
    {
      "affs": [
        1
      ],
      "name": "Kiran Luecke"
    },
    {
      "affs": [
        2
      ],
      "name": "Jack Morava"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ft8vrbm3vc2v1.bib",
  "cited_by": 10,
  "doi": "10.2140/agt.2026.26.1749",
  "fulltext_url": null,
  "id": "ft8vrbm3vc2v1",
  "issns": [
    "1472-2739",
    "1472-2747"
  ],
  "landing_url": "https://doi.org/10.2140/agt.2026.26.1749",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
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  "openalex": "W4381587493",
  "pdf_url": "https://msp.org/agt/2026/26-5/agt-v26-n5-p05-s.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-23",
  "publisher": "Mathematical Sciences Publishers",
  "ris": "https://research.draconitic.com/paper/ft8vrbm3vc2v1.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W4381587493",
      "source": "openalex",
      "url": "https://doi.org/10.2140/agt.2026.26.1749"
    }
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Homotopy and Cohomology in Algebraic Topology",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Brauer–Wall groups and truncated Picard spectra of K-theory",
  "title_text": "Brauer–Wall groups and truncated Picard spectra of K-theory",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/ft8vrbm3vc2v1",
  "venue": "Algebraic & Geometric Topology",
  "versions": []
}