{
  "abstract": "Let $\\mathcal{C}$ be a differential $\\mathbb{Z}/2$-graded category over $\\mathbb{C}$. Its periodic cyclic homology $HH^{per}_*(\\mathcal{C})$, when viewed as a vector bundle over the formal punctured disk, is equipped with a canonical connection $\\nabla^{\\mathcal{C}}_{\\partial_t}$ called the Getzler-Gauss-Manin connection in the $t$-direction (or the categorical $t$-connection). Our main result is that when $\\mathcal{C}$ is smooth and proper, this connection has a regular singularity at $t=0$ and quasi-unipotent monodromy, affirming a conjecture of Katzarkov-Kontsevich-Pantev \\cite{KKP}. Our proof follows a reduction mod $p$ argument using a spreading out technique of Toën \\cite{To} and a regularity criterion of Katz \\cite{Ka1}. The main novelty is the proof of a multiplicative property of the $p$-curvature of $\\nabla^{\\mathcal{C}}_{\\partial_t}$ through an interpretation in terms of the two-colored Kontsevich-Soibelman operad. We then explore two applications of the main result. First, we give an explicit description (under additional assumptions) of the non-commutative Hodge filtration on the periodic cyclic homology of a smooth proper d$(\\mathbb{Z}/2)$g category, following a construction of Shklyarov \\cite{Shk}. The second application, which is special to our particular method or proof, is an upper bound on the sizes of Jordan blocks of the monodromy of $\\nabla^{\\mathcal{C}}_{\\partial_t}$, which simultaneously generalizes Scherk's local monodromy theorem for isolated hypersurface singularities \\cite{Sche} and (partially) a recent result of Pomerleano-Seidel on the quantum connection of a closed monotone symplectic manifold \\cite{PS2}. As a specialization, we show that the sizes of these Jordan blocks are bounded above by the diagonal dimension of $\\mathcal{C}$ plus one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26765",
  "author_total": 1,
  "authors": [
    {
      "name": "Zihong Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7je3t8epp671z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26765",
  "fulltext_url": null,
  "id": "7je3t8epp671z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26765",
  "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.KT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7214093198",
  "pdf_url": "https://arxiv.org/pdf/2609.26765",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7je3t8epp671z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26765",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26765"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "p-curvature in non-commutative Hodge theory and the Kontsevich-Soibelman operad",
  "title_text": "p-curvature in non-commutative Hodge theory and the Kontsevich-Soibelman operad",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/7je3t8epp671z",
  "venue": "arXiv",
  "versions": []
}