{
  "abstract": "We introduce the notion of $\\mathbb{A}^1$-$n$-coverings and begin the development of their theory over an arbitrary base scheme $S$, in analogy to that of higher coverings in an $\\infty$-topos. We show that for $n=0$, our notion recovers Morel's $\\mathbb{A}^1$-coverings between simplicial sheaves. Under suitable assumptions, we then provide a Galois-theoretic classification of $\\mathbb{A}^1$-$n$-coverings. Finally, we answer a question of Morel concerning a geometric criterion for $\\mathbb{A}^1$-coverings in the negative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26345",
  "author_total": 2,
  "authors": [
    {
      "name": "Marco Giustetto"
    },
    {
      "name": "Thor Wittich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28f9pfgnkrbj8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26345",
  "fulltext_url": null,
  "id": "28f9pfgnkrbj8",
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  "landing_url": "https://arxiv.org/abs/2610.26345",
  "language": null,
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  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
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      "arxiv",
      "math.AT"
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      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7223057774",
  "pdf_url": "https://arxiv.org/pdf/2610.26345",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28f9pfgnkrbj8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26345",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26345"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the notion of $\\mathbb{A}^1$-coverings",
  "title_text": "On the notion of 𝔸^1-coverings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/28f9pfgnkrbj8",
  "venue": "arXiv",
  "versions": []
}