Rigid $G$-connections and nilpotency of $p$-curvatures

Pengfei Huang; Yichen Qin; Hao Sun

Rigid $G$-connections and nilpotency of $p$-curvatures

Algebraic Geometry 2025-12-10 v2

Authors: Pengfei Huang , Yichen Qin , Hao Sun

Abstract

Motivated by Simpson's conjecture on the motivicity of rigid irreducible connections, Esnault and Groechenig demonstrated that the mod- $p$ reductions of such connections on smooth projective varieties have nilpotent $p$ -curvatures. In this paper, we extend their result to integrable $G$ -connections.

Keywords

rigid connections G-connections p-curvature nilpotency Simpson's conjecture

Cite

@article{arxiv.2410.09929,
  title  = {Rigid $G$-connections and nilpotency of $p$-curvatures},
  author = {Pengfei Huang and Yichen Qin and Hao Sun},
  journal= {arXiv preprint arXiv:2410.09929},
  year   = {2025}
}

Comments

There is a gap about the horizontality of the Hitchin morphism on higher dimensional varieties. In this version, we only focus on the case of curves

Rigid $G$-connections and nilpotency of $p$-curvatures

Abstract

Keywords

Cite

Comments

Related papers