Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on cycle classes of sections of the arithmetic fundamental group   Given a smooth and separated K(pi,1) variety X over a field k, we associate a
"cycle class" in etale cohomology with compact supports to any continuous
section of the natural map from the arithmetic fundamental group of X to the
absolute Galois group of k. We discuss the algebraicity of this class in the
case of curves over p-adic fields, and deduce in particular a new proof of
Stix's theorem according to which the index of a curve X over a p-adic field k
must be a power of p as soon as the natural map from the arithmetic fundamental
group of X to the absolute Galois group of k admits a section. Finally, an
etale adaptation of Beilinson's geometrization of the pronilpotent completion
of the topological fundamental group allows us to lift this cycle class in
suitable cohomology groups.

13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
1
The categories of this paper are: cs
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph