{
  "abstract": "We prove that for any prime $p$ and tame level $N$, the weight map from the cuspidal Hilbert eigenvariety constructed by Andreatta-Iovita-Pilloni for a totally real field $F$ to the weight space is proper in the sense of Buzzard-Calegari, under a non-vanishing hypothesis on certain Sen polynomials of Galois representations at the primes above $p$. In particular, this yields the properness of the eigenvariety away from non-positive integral Sen weights. Our approach extends the $p$-adic Hodge-theoretic argument of Diao-Liu.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12605",
  "author_total": 1,
  "authors": [
    {
      "name": "Yi Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0jhn8tzv0wnrr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12605",
  "fulltext_url": null,
  "id": "0jhn8tzv0wnrr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12605",
  "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.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221537581",
  "pdf_url": "https://arxiv.org/pdf/2610.12605",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0jhn8tzv0wnrr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12605",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12605"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Properness of the Cuspidal Hilbert Eigenvariety",
  "title_text": "Properness of the Cuspidal Hilbert Eigenvariety",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/0jhn8tzv0wnrr",
  "venue": "arXiv",
  "versions": []
}