  It is conjectured by de Jong that, if $X$ is a connected projective smooth
variety over an algebraically closed field $k$ of characteristic $p>0$ with
trivial etale fundamental group, any convergent isocrystal $\mathcal{E}$ on $X$
is trivial. We discuss this conjecture when $X$ is liftable to characteristic
zero, and prove the triviality of $\mathcal{E}$ in this case under certain
conditions on (semi)stability.
