Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stratified bundles and \'etale fundamental group   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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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph