Core Concepts
This research paper proves that the mod-p reductions of rigid integrable G-connections on smooth projective varieties have nilpotent p-curvatures, extending previous results for regular connections and providing further evidence for Simpson's motivicity conjecture.
Quotes
"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."
"Simpson addressed this transcendental nature in [Sim90], where he posed a question about which integrable connections defined over Q have associated monodromy representations also defined over Q. He conjectured that such integrable connections should originate from geometry"
"In this paper, we aim to generalize Esnault–Groechenig’s result on nilpotency of p-curvatures [EG20, Theorem 1.4] to rigid integrable G-connections."