{
  "abstract": "We introduce the notion of a naive global 2-ring: a functor from the opposite of the normal infinity ∞ $\\infty$ -category of global spaces to presentably symmetric monoidal stable normal infinity ∞ $\\infty$ -categories. By passing to global sections, every naive global 2-ring decategorifies to a multiplicative cohomology theory on global spaces, i.e. a naive global ring. We suggest when a naive global 2-ring deserves to be called genuine . As evidence, we associate to such a global 2-ring a family of equivariant cohomology theories which satisfy a version of the change-of-group axioms introduced by Ginzburg, Kapranov, and Vasserot [V. Ginzburg, M. Kapranov and E. Vasserot, Elliptic algebras and equivariant elliptic cohomology , Preprint (1995), arXiv:q-alg/9505012 ]. We further show that the decategorified multiplicative global cohomology theory associated to a genuine global 2-ring canonically refines to an double struck upper E Subscript normal infinity E ∞ $\\mathbb{E}_\\infty$ -ring object in global spectra. As we show, two interesting examples of genuine global 2-rings are given by quasi-coherent sheaves on the torsion points of an oriented spectral elliptic curve and Lurie s theory of tempered local systems. In particular, we obtain global spectra representing equivariant elliptic cohomology and tempered cohomology.",
  "abstract_shown": true,
  "affiliations": [
    "Johns Hopkins University",
    "Universität Regensburg",
    "Max Plank Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "David Gepner",
      "orcid": "0000-0002-7825-9579"
    },
    {
      "affs": [
        1
      ],
      "name": "Sil Linskens",
      "orcid": "0000-0002-2604-4875"
    },
    {
      "affs": [
        2
      ],
      "name": "Luca Pol",
      "orcid": "0000-0003-1105-0137"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/719698ah5y8m6.bib",
  "cited_by": 12,
  "doi": "10.1017/s0010437x26102875",
  "fulltext_url": null,
  "id": "719698ah5y8m6",
  "issns": [
    "0010-437X",
    "1570-5846"
  ],
  "landing_url": "https://doi.org/10.1017/s0010437x26102875",
  "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"
    ]
  ],
  "openalex": "W4400480151",
  "pdf_url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/12A72980A63324E79CD0E4B992925E32/S0010437X26102875a.pdf/div-class-title-global-2-rings-and-genuine-refinements-div.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-01",
  "publisher": "Cambridge University Press",
  "ris": "https://research.draconitic.com/paper/719698ah5y8m6.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T13:20:36Z",
      "native_id": "W4400480151",
      "source": "openalex",
      "url": "https://doi.org/10.1017/s0010437x26102875"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Homotopy and Cohomology in Algebraic Topology",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Global 2-rings and genuine refinements",
  "title_text": "Global 2-rings and genuine refinements",
  "type": "peer-reviewed",
  "updated_at": "2026-11-10T13:20:57Z",
  "url": "https://research.draconitic.com/paper/719698ah5y8m6",
  "venue": "Compositio Mathematica",
  "versions": []
}