{
  "annotation_id": "955780a7-dbfe-4054-a0b8-852fa1ad5c94",
  "date_created": "2026-02-17T05:53:12.332000Z",
  "date_modified": "2026-02-17T05:53:12.332000Z",
  "file_hash": "f62348a9e5d52c4bbfddaef301f507072241aacaf91eeb7d7bdd6277ff49e8a3",
  "private": false,
  "record": {
    "abstract": "Let $X\\to S$ be a smooth projective morphism. Katz proved the Grothendieck-Katz $p$-curvature conjecture for the Gauss-Manin connection on the $i$-th cohomology of $X/S$: if its $p$-curvature vanishes mod $p$ for infinitely many $p$, then the action of $\\pi_1(S,s)$ on $H^i(X_s, \\mathbb{Z})$ factors through a finite group. We prove a non-abelian analogue of this statement: if the $p$-curvature of the isomonodromy foliation on the moduli of flat bundles of rank $r$ on $X/S$ vanishes mod $p$ for infinitely many $p$, then the action of $\\pi_1(S,s)$ on the rank $r$ integral characters of $\\pi_1(X_s)$ factors through a finite group. We deduce many new cases of the Bost/Ekedahl--Shepherd-Barron--Taylor conjecture.\n  The proofs rely on a non-abelian version of Katz\u0027s formula, and a non-abelian version of the Hodge index theorem.",
    "arxiv_id": "2601.07933",
    "authors": [
      "Yeuk Hay Joshua Lam",
      "Daniel Litt"
    ],
    "categories": [
      "math.AG",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "p-Curvature and Non-Abelian Cohomology",
    "url": "https://arxiv.org/abs/2601.07933",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0c076454-35bd-4a0c-8d1a-a5438c3f05b2",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}