TY - JOUR
T1 - The Brauer-Manin pairing, class field theory, and motivic homology
AU - Yamazaki, Takao
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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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U2 - 10.1215/00277630-2077008
DO - 10.1215/00277630-2077008
M3 - Article
AN - SCOPUS:84879245497
VL - 210
SP - 29
EP - 58
JO - Nagoya Mathematical Journal
JF - Nagoya Mathematical Journal
SN - 0027-7630
ER -