{
  "abstract": "We establish a global equivariant refinement of the theorem of Snaith that presents the complex $K$-theory spectrum as a localization of the suspension spectrum of $\\mathbb C P^\\infty$. We prove that the morphism of ultra-commutative global ring spectra from $Σ^\\infty_+ B_{\\text{gl}} U(1)$ that classifies the tautological $U(1)$-representation exhibits the global $K$-theory spectrum as a specific localization, in both the $\\infty$-categories of ultra-commutative ring spectra and of commutative global ring spectra. The classes to be inverted are certain representation-graded $U(n)$-equivariant homotopy classes of $Σ^\\infty_+ B_{\\text{gl}} U(1)$, the pre-Bott classes. We also show that for every compact Lie group $G$, the $G$-equivariant $K$-theory spectrum is a telescopic localization of $Σ^\\infty_+ B_G U(1)$ by the pre-Bott classes of all unitary $G$-representations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21675",
  "author_total": 1,
  "authors": [
    {
      "name": "Stefan Schwede"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9377gm0wht3es.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21675",
  "fulltext_url": null,
  "id": "9377gm0wht3es",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21675",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7222608638",
  "pdf_url": "https://arxiv.org/pdf/2610.21675",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9377gm0wht3es.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21675",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21675"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Equivariant $K$-theory as a global localization",
  "title_text": "Equivariant K-theory as a global localization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/9377gm0wht3es",
  "venue": "arXiv",
  "versions": []
}