{
  "abstract": "A fundamental question in $p$-adic symplectic geometry and $p$-adic Hamiltonian mechanics is to what extent we can learn new information about integrable systems with coefficients in the rational numbers $\\mathbb{Q}$, if we view them as $p$-adic systems instead of real ones. We combine geometric analytic estimates with Galois theory in order to show that at a local level, these real and $p$-adic viewpoints give completely different information. Then we focus on understanding this local behavior for the $p$-adic case by proving effective methods to compute local normal forms. Our results are motivated by a program outlined by Pelayo-Voevodsky-Warren a decade ago, to develop a $p$-adic theory of integrable systems and symplectic geometry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.24363",
  "author_total": 2,
  "authors": [
    {
      "name": "Luis Crespo"
    },
    {
      "name": "Álvaro Pelayo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/acgndmw2drbps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.24363",
  "fulltext_url": null,
  "id": "acgndmw2drbps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.24363",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2610|advanced mathematical theories"
    ]
  ],
  "openalex": "W7165809053",
  "pdf_url": "https://arxiv.org/pdf/2606.24363",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/acgndmw2drbps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2606.24363",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.24363"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The contrast between real and $p$-adic integrability",
  "title_text": "The contrast between real and p-adic integrability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/acgndmw2drbps",
  "venue": "arXiv",
  "versions": []
}