{
  "abstract": "The construction of a $p$-adic height pairing for a geometric $p$-adic representation of the absolute Galois group of a number field depends on a global $p$-adic logarithm and on local splittings of the Hodge filtrations at the primes above $p$. We study the dependence on these splittings for suitable two-dimensional symplectic self-dual representations, including self-dual twists of representations attached to even-weight newforms at non-ordinary primes not dividing the level. We express the difference between the height pairings associated with the two splittings determined by Frobenius explicitly in terms of local Bloch--Kato logarithms. As an application over $\\mathbb{Q}$, we prove that at least one of the two cyclotomic $p$-adic height pairings is non-trivial under the additional assumptions that the Frobenius eigenvalues at $p$ are distinct and the localization map at $p$ from the Bloch--Kato Selmer group is non-zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35626",
  "author_total": 3,
  "authors": [
    {
      "name": "Taiga Adachi"
    },
    {
      "name": "Yu Katagiri"
    },
    {
      "name": "Ryota Shii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2r3qrvab3e24p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35626",
  "fulltext_url": null,
  "id": "2r3qrvab3e24p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35626",
  "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": "W7214736107",
  "pdf_url": "https://arxiv.org/pdf/2609.35626",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2r3qrvab3e24p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35626",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35626"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A difference formula of $p$-adic height pairings via the Bloch-Kato logarithm map",
  "title_text": "A difference formula of p-adic height pairings via the Bloch-Kato logarithm map",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/2r3qrvab3e24p",
  "venue": "arXiv",
  "versions": []
}