Grothendieck-Katz conjecture

Abstract

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 ${\rm ord}_pm!\geq k$. This provides us with a reformulation of Grothendieck-Katz conjecture with stronger hypothesis.