{
  "abstract": "We revisit fixed-point localization techniques in equivariant topological $K$-theory, presenting its fibers over varying points of the equivariant base as cohomology of the corresponding fixed-point schemes. We then employ this framework for an effective description of the equivariant $K$-theory ring of the affine Grassmannian $\\mathcal{G}r_G$. We do so by a detailed study of the relevant fixed points, extending known results to the action of any $(x, ζ) \\in T \\times \\mathbb{G}_{m}^{\\mathrm{rot}}$. We obtain a description of the complexified topological $K$-theory ring $K^{\\mathrm{top}, 0}_{T\\times \\mathbb{G}_{m}^{\\mathrm{rot}}}(\\mathcal{G}r_G; \\mathbb{C})$ as the ring of functions on a family of affine blowups, extending and proving a conjecture of Roman Bezrukavnikov. While this ring is fairly big, we provide a preferred infinite set of topological generators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12889",
  "author_total": 1,
  "authors": [
    {
      "name": "Jakub Löwit"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/66rkpxe154hqx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12889",
  "fulltext_url": null,
  "id": "66rkpxe154hqx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12889",
  "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.AG"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7212490883",
  "pdf_url": "https://arxiv.org/pdf/2609.12889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/66rkpxe154hqx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12889"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Equivariant $K$-theory ring of the affine Grassmannian as deformation to normal cone",
  "title_text": "Equivariant K-theory ring of the affine Grassmannian as deformation to normal cone",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/66rkpxe154hqx",
  "venue": "arXiv",
  "versions": []
}