Stratified bundles and étale fundamental group (new version)

This submission replaces the arXiv:1012.5381 submission with the same title, which had been withdrawn as it contained a mistake, repaired in this submission: on $X$ projective smooth over an algebraically closed field of characteristic $p>0$, we show that all irreducible stratified bundles have rank 1 if and only if the commutator $[π_1, π_1]$ of the étale fundamental group $π_1$ 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 $π_1$ is abelian without $p$-power quotient. This answers positively a conjecture by Gieseker.

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