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The Brauer–Manin pairing, class field theory, and motivic homology
Published online by Cambridge University Press: 11 January 2016
Abstract
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.
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- Research Article
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2013
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