{
  "abstract": "We show that integers act invertibly on a derived scheme $S$ if and only if they act invertibly on the reduced motivic suspension spectrum of the affine line in $\\mathrm{MS}_S$. As a consequence, over regular locally noetherian schemes and derived schemes on which some nonzero integer acts as zero, the motivic sphere spectrum is $\\mathbf{A}^1$-invariant after inverting primes that are not invertible in the base scheme. In particular, over regular locally noetherian $\\mathbf{Q}$-schemes, the motivic sphere spectrum is $\\mathbf{A}^1$-invariant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11802",
  "author_total": 1,
  "authors": [
    {
      "name": "Viktor Burghardt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dw951b2wx9qnz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11802",
  "fulltext_url": null,
  "id": "dw951b2wx9qnz",
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  "landing_url": "https://arxiv.org/abs/2610.11802",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
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      "arxiv",
      "math.KT"
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      "2610|Homotopy and Cohomology in Algebraic Topology"
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  ],
  "openalex": "W7221097246",
  "pdf_url": "https://arxiv.org/pdf/2610.11802",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dw951b2wx9qnz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11802",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11802"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Loyalty of the affine line in motivic homotopy theory",
  "title_text": "Loyalty of the affine line in motivic homotopy theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/dw951b2wx9qnz",
  "venue": "arXiv",
  "versions": []
}