3 problems

Simpson's motivicity conjecture. Rigid integrable connections are motivic.

Simpson's standard conjecture. By spreading out, the $\overline{\mathbb{Q}}$-points in the intersection

Grothendieck's p-curvature conjecture. If $M$ satisfies $\frak{P}$, then there exists a finite étale cover $h:Y\to X$ such that $h^*M$ is trivial as a connection; equivalently, $M$…