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arXiv · 2410.09929

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

Pengfei Huang·Yichen Qin·Hao Sun
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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.

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Pengfei Huang, Yichen Qin, Hao Sun. 2024-10-13. Rigid $G$-connections and nilpotency of $p$-curvatures. https://arxiv.org/abs/2410.09929

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