{
  "abstract": "We study $KU_G$-localization for finite groups. For a finite nilpotent group $G$, we identify the $KU_G/p$-local sphere as the fiber of an Adams operation, and reduce the computation of its homotopy Mackey functors to the corresponding computation for the Sylow $p$-subgroup of $G$. At the prime $2$, we compute $\\underlineπ_* L_{KU_G/2}S_G$ for abelian $2$-groups, resolve the resulting extension problems, and determine the degree-zero Hurewicz image. As a consequence, we completely determine the $\\mathbb Z$-graded homotopy Mackey functors of $L_{KU_G}S_G$ for all finite abelian groups. Finally, for an arbitrary finite group $G$, we prove that the $KU_G/p$-localization of $G$-spectra splits as a wedge of height-one equivariant Morava $K$-localizations, indexed by conjugacy classes of cyclic subgroups of order prime to $p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.30285",
  "author_total": 1,
  "authors": [
    {
      "name": "Yingxin Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cr0tp10j4w908.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.30285",
  "fulltext_url": null,
  "id": "cr0tp10j4w908",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.30285",
  "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": "W7162773296",
  "pdf_url": "https://arxiv.org/pdf/2605.30285",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cr0tp10j4w908.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2605.30285",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.30285"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the equivariant $KU_G$-local sphere for finite abelian groups",
  "title_text": "On the equivariant KU_G-local sphere for finite abelian groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/cr0tp10j4w908",
  "venue": "arXiv",
  "versions": []
}