{
  "abstract": "The main result determines the zeroth integral Milnor-Witt stem of the motivic sphere spectrum in the Morel-Voevodsky motivic stable homotopy category of the integers. The component in weight zero is the Grothendieck-Witt ring of nondegenerate symmetric bilinear forms over the integers. Along the way, cellularity of connective Witt theory, as well as an absolute purity result for the η-inverted motivic sphere spectrum, is established over Dedekind domains of mixed characteristic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03069",
  "author_total": 1,
  "authors": [
    {
      "name": "Oliver Röndigs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6z82ed2ecbqh6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03069",
  "fulltext_url": null,
  "id": "6z82ed2ecbqh6",
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  "landing_url": "https://arxiv.org/abs/2610.03069",
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
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      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7220417310",
  "pdf_url": "https://arxiv.org/pdf/2610.03069",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6z82ed2ecbqh6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.03069",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03069"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The zeroth stable homotopy groups of motivic spheres over the integers",
  "title_text": "The zeroth stable homotopy groups of motivic spheres over the integers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/6z82ed2ecbqh6",
  "venue": "arXiv",
  "versions": []
}