Stratified bundles and étale fundamental group

Details Stratified bundles and étale fundamental group Stratified bundles and étale fundamental group

2010-12-24

arxiv.org/abs/1012.5381v3

Mathematics

Algebraic Geometry

We thank the referee who pointed out that p.7 displayed formula is wrong. We therefore withdraw the article. Lem 3.2 is proven

Scientific paper

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.

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