p-Curvature and Non-Abelian Cohomology

Yeuk Hay Joshua Lam, Daniel Litt

Let $X\to S$ be a smooth projective morphism. Katz proved the Grothendieck-Katz $p$-curvature conjecture for the Gauss-Manin connection on the $i$-th cohomology of $X/S$: if its $p…