  Let $X_0$ be a smooth geometrically connected variety defined over a finite
field $\mathbb F_q$ and let $\mathcal E_0^{\dagger}$ be an irreducible
overconvergent $F$-isocrystal on $X_0$. We show that if a subobject of minimal
slope of the associated convergent $F$-isocrystal $\mathcal E_0$ admits a
non-zero morphism to $\mathcal O_{X_0}$ as a convergent isocrystal, then
$\mathcal E_0^{\dagger}$ is isomorphic to $\mathcal O^{\dagger}_{X_0}$ as an
overconvergent isocrystal. This proves a special case of a conjecture of
Kedlaya. The key ingredient in the proof is the study of the monodromy group of
$\mathcal E_0^{\dagger}$ and the subgroup defined by $\mathcal E_0$. The new
input in this setting is that the subgroup contains a maximal torus of the
entire monodromy group. This is a consequence of the existence of a Frobenius
torus of maximal dimension. As an application, we prove a finiteness result for
the torsion points of abelian varieties, which extends the previous theorem of
Lang--N\'eron and answers positively a question of Esnault.
