Grothendieck-Katz conjecture

In this article we prove that linear differential equations with only algebraic solutions have zero $m$-curvature modulo $p^k$ for all except a finite number of primes $p$ and all $k,m\in \mathbb{N}$ with ${\mathrm{o}\mathrm{r}\mathrm{d}}_{p}m!\ge k$. This provides us with a reformulation of Grothendieck-Katz conjecture with stronger hypothesis.