Brauer-Manin pairing, class field theory and motivic homology

Details Brauer-Manin pairing, class field theory and motivic homology Brauer-Manin pairing, class field theory and motivic homology

2010-09-21

arxiv.org/abs/1009.4026v5

Mathematics

Number Theory

25 pages

Scientific paper

For a smooth proper variety over a $p$-adic field, the Brauer group and
abelian fundamental group are related to the higher Chow groups by the
Brauer-Manin pairing and the class field theory. We generalize this relation to
smooth (possibly non-proper) varieties, using the motivic homology and the tame
version of Wiesend's ideal class group. Several examples are discussed.

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