{
  "abstract": "Let $X$ be a proper smooth rigid analytic variety over a complete algebraically closed $p$-adic field $\\mathbf C$. Fix a continuation $\\operatorname{Exp}$ of $\\exp$. Faltings, in the curve case, and Heuer showed that any lifting $\\widetilde X$ of $X$ over $B_{\\mathrm{dR}}^+/t^2$ induces an equivalence between the category of Higgs bundles on $X_{\\text{ét}}$ and the category of $v$-vector bundles on $X_v$. Changing $\\widetilde X$ is known to alter the correspondence nontrivially. This raises the natural question of how the isomorphism class of the Higgs bundle associated with a fixed $v$-vector bundle varies with $\\widetilde X$, a question that has not been systematically studied. In this paper, we address this question when $X$ is a curve of genus $g\\ge 2$. More precisely, we call a Higgs bundle lift-independent if it corresponds to the same $v$-bundle under the $p$-adic Simpson correspondence for every lifting $\\widetilde X$. We prove the following results. (1) Every lift-independent Higgs bundle of rank $r\\le g$ is nilpotent. (2) Every semistable lift-independent Higgs bundle of rank $r\\le \\sqrt{g}+1$ has zero Higgs field. (3) In contrast, vanishing fails even within the class singled out by Faltings' conjecture: there always exists a lift-independent semistable Higgs bundle of degree $0$ with nonzero Higgs field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.29947",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiangyu Pan"
    },
    {
      "name": "Jiahong Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ffcwvdhamf71.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.29947",
  "fulltext_url": null,
  "id": "0ffcwvdhamf71",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.29947",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7162790705",
  "pdf_url": "https://arxiv.org/pdf/2605.29947",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ffcwvdhamf71.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2605.29947",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.29947"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lift-independence problem in the $p$-adic Simpson correspondence for curves",
  "title_text": "Lift-independence problem in the p-adic Simpson correspondence for curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/0ffcwvdhamf71",
  "venue": "arXiv",
  "versions": []
}