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

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.

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