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The Brauer–Manin pairing, class field theory, and motivic homology

Published online by Cambridge University Press:  11 January 2016

Takao Yamazaki*
Affiliation:
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan, [email protected]
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Abstract

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

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2013

References

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