{
  "abstract": "We prove the strong local monodromy conjecture for poles of order at least $n-1$ of the naive motivic zeta-function for a complex polynomial of $n$ variables. Moreover, for every such pole $s$, we construct an explicit homology $\\exp(2πi s)$-eigencycle in a neighborhood of any given 1-dimensional exceptional stratum contributing the pole. The proof combines topological techniques developed by the author with a fact of birational geometry discovered by AI.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22111",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Esterov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1q8crpcje4ycw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22111",
  "fulltext_url": null,
  "id": "1q8crpcje4ycw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22111",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222413021",
  "pdf_url": "https://arxiv.org/pdf/2610.22111",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1q8crpcje4ycw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22111",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22111"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The monodromy conjecture for high order poles, and norms of residue antiderivatives",
  "title_text": "The monodromy conjecture for high order poles, and norms of residue antiderivatives",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/1q8crpcje4ycw",
  "venue": "arXiv",
  "versions": []
}