{
  "abstract": "Following Macintyre's quantifier elimination result for semi-algebraic $p$-adic sets from 1976, Denef's cell decomposition from 1984 has played a catalyzing role for both motivic integration and Hensel minimality. Motivic integration has in turn been applied in the Langlands program via transfer principles to change the characteristic of the local field, e.g., for the fundamental lemma. Hensel minimality has been used to study rational points on definable sets, providing non-archimedean analogues of results by Pila and Wilkie in o-minimal structures. I will review some related results and open questions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Proceedings of the International Congress of Mathematicians 2026 - Volume 3: Invited Lectures (Sections 1-4) Pages 41 - 56",
  "arxiv": "2610.09852",
  "author_total": 1,
  "authors": [
    {
      "name": "Raf Cluckers"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9x5zetysp6veb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09852",
  "fulltext_url": null,
  "id": "9x5zetysp6veb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09852",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.09852",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9x5zetysp6veb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09852",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09852"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "From Cell Decomposition to Motivic Integration, Hensel Minimality, and Point Counting",
  "title_text": "From Cell Decomposition to Motivic Integration, Hensel Minimality, and Point Counting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/9x5zetysp6veb",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1137/25m180545x",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}