{
  "abstract": "Given an abelian scheme $A$ over a $p$-adic ring $R$, Borger and Saha constructed a filtered module $\\{\\mathbf{H}_δ(A) \\supset \\mathbf{X}_{\\mathrm{prim}}(A)\\supset \\{0\\}\\}$ with a semilinear operator $\\mathfrak{f}^*$ on $\\mathbf{H}_δ(A)$ using the theory of arithmetic jet spaces. The above object admits a canonical map $Φ$ to the Hodge sequence $\\{\\mathbf{H}^1_{\\mathrm{dR}}(A) \\supset H^0(A,Ω_A)\\supset \\{0\\}\\}$ of $A$ in the category of filtered modules. As a result, by restricting $Φ$, we obtain a natural $R$-linear map $Υ: \\mathbf{X}_{\\mathrm{prim}}(A) \\rightarrow H^0(A,Ω_A)$. In this paper, we show that the map $Υ$ is an isomorphism of vector spaces over $K$, the field of fractions of $R$. As a consequence, we will show that for all abelian schemes $A$, the operator $\\mathfrak{f}^*$ on $\\mathbf{H}_δ(A)_K$ is a bijection, and our object $\\{\\mathbf{H}_δ(A)_K \\supset \\mathbf{X}_{\\mathrm{prim}}(A)_K\\supset \\{0\\}\\}$ becomes a filtered isocrystal. In fact, the above results admit a generalization to the setting of semi-abelian schemes. The elements of $\\mathbf{X}_{\\mathrm{prim}}(A)$ are represented by primitive additive characters of the arithmetic jet spaces attached to $A$. Hence, our isomorphism given by $Υ$ provides an interesting character-theoretic interpretation of $H^0(A,Ω_A)$ in terms of primitive delta characters. As a result, to any $1$-form $ω$, the above isomorphism associates a canonical numerical invariant that depends on deformation theoretic data of $A$. Furthermore, we also extend a comparison theorem between $\\mathbf{H}_δ(A)_K$ and the first crystalline cohomology $\\mathbf{H}_{\\mathrm{cris}}^1(A)_K$ in the general case when the elliptic curve $A$ is defined over the ring of integers of a $p$-adic field $K$ that is a finite extension of $\\mathbb{Q}_p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28365",
  "author_total": 3,
  "authors": [
    {
      "name": "Lance Gurney"
    },
    {
      "name": "Sudip Pandit"
    },
    {
      "name": "Arnab Saha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/97exkd8zz1mve.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28365",
  "fulltext_url": null,
  "id": "97exkd8zz1mve",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28365",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214191128",
  "pdf_url": "https://arxiv.org/pdf/2609.28365",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/97exkd8zz1mve.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28365",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28365"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Delta Characters and Filtered Isocrystals",
  "title_text": "Delta Characters and Filtered Isocrystals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/97exkd8zz1mve",
  "venue": "arXiv",
  "versions": []
}