{
  "abstract": "We show that several Dold-Kan type equivalences can be understood as a passage from constructible sheaves on symmetric products (i.e. spaces of polynomials) to polynomial sheaves in the sense of Goodwillie-Weiss calculus, by means of a natural analytic expansion functor. This geometric perspective provides access to standard tools from sheaf theory such as the six functor formalism and $t$-structures. For example, the equivalence between filtered objects and coherent chain complexes in a stable $\\infty$-category receives a geometric incarnation as Verdier duality between $!$-sheaves and $*$-cosheaves on an $\\infty$-dimensional simplex. As a main application, we obtain an intrinsic geometric explanation for the appearance of vanishing cycle data for perverse sheaves in a paracyclic variant of the Dold--Kan correspondence pioneered by Dwyer and Kan, at the same time lifting their equivalence to stable $\\infty$-categories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36314",
  "author_total": 3,
  "authors": [
    {
      "name": "Tobias Dyckerhoff"
    },
    {
      "name": "Till Heine"
    },
    {
      "name": "Simon Schneider"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ya37yp5pka4f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36314",
  "fulltext_url": null,
  "id": "1ya37yp5pka4f",
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  "landing_url": "https://arxiv.org/abs/2610.36314",
  "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.CT"
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      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7224135882",
  "pdf_url": "https://arxiv.org/pdf/2610.36314",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ya37yp5pka4f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36314",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36314"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sheaves on polynomials and polynomial sheaves",
  "title_text": "Sheaves on polynomials and polynomial sheaves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/1ya37yp5pka4f",
  "venue": "arXiv",
  "versions": []
}