Mathematics – Algebraic Geometry
Scientific paper
2011-12-20
Mathematics
Algebraic Geometry
This submission replaces the arXiv:1012.5381 submission with the same title, which had been withdrawn as it contained a mistak
Scientific paper
This submission replaces the arXiv:1012.5381 submission with the same title, which had been withdrawn as it contained a mistake, repaired in this submission: on $X$ projective smooth over an algebraically closed field of characteristic $p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 $[\pi_1, \pi_1]$ of the \'etale fundamental group $\pi_1$ 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 $ \pi_1 $ is abelian without $p$-power quotient. This answers positively a conjecture by Gieseker.
Esnault Hélène
Sun Xiaotao
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