Nagoya Mathematical Journal

The 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, 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.

Article information

Source
Nagoya Math. J., Volume 210 (2013), 29-58.

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1369058027

Digital Object Identifier
doi:10.1215/00277630-2077008

Mathematical Reviews number (MathSciNet)
MR3079274

Zentralblatt MATH identifier
1325.11125

Subjects
Primary: 11S25: Galois cohomology [See also 12Gxx, 16H05]
Secondary: 14G20: Local ground fields 14C25: Algebraic cycles

Citation

Yamazaki, Takao. The Brauer–Manin pairing, class field theory, and motivic homology. Nagoya Math. J. 210 (2013), 29--58. doi:10.1215/00277630-2077008. https://projecteuclid.org/euclid.nmj/1369058027


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