  v2: A few typos corrected, a few formulations improved.
  On $X$ projective smooth over an algebraically closed field of characteristic
$p>0$, we show that irreducible stratified bundles have rank 1 if and only if
the commutator $[\pi_1^{{\rm \acute{e}t}}, \pi_1^{{\rm \acute{e}t}}]$ of the
\'etale fundamental group is a pro-$p$-group, and we show that the category of
stratified bundles is semi-simple with irreducible objects of rank 1 if and
only if $ \pi_1^{{\rm \acute{e}t}}$ is abelian without $p$-power quotient. This
answers positively a conjecture by Gieseker.
