Local-global principle for certain biquadratic normic bundles

Yang Cao, and Yongqi Liang. "Local-global principle for certain biquadratic normic bundles." Acta Arithmetica 164.2 (2014): 137-144. <http://eudml.org/doc/286627>.

@article{YangCao2014,
abstract = {Let X be a proper smooth variety having an affine open subset defined by the normic equation $N_\{k(√a,√b)/k\}(x) = Q(t₁,..., tₘ)²$ over a number field k. We prove that: (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of X; (2) the analogue for rational points is also valid assuming Schinzel’s hypothesis.},
author = {Yang Cao, Yongqi Liang},
journal = {Acta Arithmetica},
keywords = {zero-cycles; rational points; local-global principle; Hasse principle; weak approximation; Brauer-Manin obstruction; normic equations},
language = {eng},
number = {2},
pages = {137-144},
title = {Local-global principle for certain biquadratic normic bundles},
url = {http://eudml.org/doc/286627},
volume = {164},
year = {2014},
}

TY - JOUR
AU - Yang Cao
AU - Yongqi Liang
TI - Local-global principle for certain biquadratic normic bundles
JO - Acta Arithmetica
PY - 2014
VL - 164
IS - 2
SP - 137
EP - 144
AB - Let X be a proper smooth variety having an affine open subset defined by the normic equation $N_{k(√a,√b)/k}(x) = Q(t₁,..., tₘ)²$ over a number field k. We prove that: (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of X; (2) the analogue for rational points is also valid assuming Schinzel’s hypothesis.
LA - eng
KW - zero-cycles; rational points; local-global principle; Hasse principle; weak approximation; Brauer-Manin obstruction; normic equations
UR - http://eudml.org/doc/286627
ER -