{
  "abstract": "Using the framework of delta characters on arithmetic jet spaces, we construct a canonical sequence of filtered isocrystals associated to an abelian scheme $A$ of relative dimension $g$ over a $p$-adically complete discrete valuation ring. These isocrystals map injectively via a canonical morphism into the first (rational) crystalline cohomology group $\\mathbf{H}^1_{\\mathrm{cris}}(A)$ of the abelian scheme $A$, directly generalizing a prior construction due to Borger and Saha. Pandit showed that the canonical morphism is a map of isocrystals. This then implies that the image of this canonical embedding coincides with the minimal subisocrystal $F_{\\mathrm{cris}}(Ω_A)$ containing the space of invariant differential forms $H^0(A,Ω_A)$. Berthelot and Ogus showed that the dimension of $F_{\\mathrm{cris}}(Ω_A)$ is $g$ if and only if $A$ has an endomorphism that lifts the absolute Frobenius on the special fiber of $A$. As a primary application, for a general abelian scheme $A$, we show that the minimal subisocrystal $F_{\\mathrm{cris}}(Ω_A)$ can be viewed as a module obtained from primitive delta characters of $A$ via appropriate twists by the canonical Frobenius morphism $ϕ$ induced from the theory of arithmetic jet spaces. As a consequence, we show that the rank of $F_{\\mathrm{cris}}(Ω_A)$ depends on numerical invariants arising from the theory of delta characters of $A$. More precisely, the dimension of $F_{\\mathrm{cris}}(Ω_A)$ is given by the sum of the exact orders of the primitive delta characters associated to the abelian scheme $A$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33948",
  "author_total": 2,
  "authors": [
    {
      "name": "Rajat Kumar Mishra"
    },
    {
      "name": "Arnab Saha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85wb3b7h4ddve.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33948",
  "fulltext_url": null,
  "id": "85wb3b7h4ddve",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33948",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223995868",
  "pdf_url": "https://arxiv.org/pdf/2610.33948",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/85wb3b7h4ddve.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33948",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33948"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Delta Characters and Ranks of Minimal Subisocrystals of Abelian Schemes",
  "title_text": "Delta Characters and Ranks of Minimal Subisocrystals of Abelian Schemes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/85wb3b7h4ddve",
  "venue": "arXiv",
  "versions": []
}