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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
Takao Yamazaki*
Affiliation:
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan, ytakao@math.tohoku.ac.jp
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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

11S2514G2014C25
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 210 , June 2013 , pp. 29 - 58
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2013

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