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

Takao Yamazaki

doi:10.1215/00277630-2077008

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

Takao Yamazaki

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	29-58
Number of pages	30
Journal	Nagoya Mathematical Journal
Volume	210
DOIs	https://doi.org/10.1215/00277630-2077008
Publication status	Published - 2013 Jun 26

ASJC Scopus subject areas

Mathematics(all)

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