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arXiv · 1009.4026

Brauer-Manin pairing, class field theory and motivic homology

Takao Yamazaki
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Abstract

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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Takao Yamazaki. 2010-09-21. Brauer-Manin pairing, class field theory and motivic homology. https://doi.org/10.1215/00277630-2077008

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