{
  "abstract": "Let $F$ be an absolutely unramified mixed characteristic local field with rings of integers $O_F$. For a small affine algebra $R$ over $O_F$, we consider the logarithmic étale fundamental group $G_R$ of its generic fibre equipped with a \"horizontal\" log-structure, in the sense of Fujiwara--Kato. We study $p$-adic representations of $G_R$ and obtain a classification of these representations in terms of étale $(φ, Γ_R)$-modules. Moreover, we define and study the notion of log-crystalline representations of $G_R$, a generalisation of crystalline representations from the non-logarithmic/smooth case. Furthermore, in the logarithmic setting, we show that log-crystalline representations of $G_R$ are equivalent to Wach modules for $R$, extending our previous results from the (non-logarithmic) crystalline case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11266",
  "author_total": 2,
  "authors": [
    {
      "name": "Abhinandan"
    },
    {
      "name": "Denis Benois"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8d1r516vba16b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11266",
  "fulltext_url": null,
  "id": "8d1r516vba16b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11266",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7212272974",
  "pdf_url": "https://arxiv.org/pdf/2609.11266",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8d1r516vba16b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11266",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11266"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Log-crystalline representations and $(φ, Γ)$-modules",
  "title_text": "Log-crystalline representations and $(φ, Γ)$-modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/8d1r516vba16b",
  "venue": "arXiv",
  "versions": []
}