Local-global principle for certain biquadratic normic bundles
Volume 164 / 2014
Acta Arithmetica 164 (2014), 137-144
MSC: Primary 11G35; Secondary 14G25, 14G05, 14D10, 14C25.
DOI: 10.4064/aa164-2-3
Abstract
Let $X$ be a proper smooth variety having an affine open subset defined by the normic equation $N_{k(\sqrt {a},\sqrt {b})/k}({\textbf {x}})=Q(t_{1},\ldots ,t_{m})^{2}$ 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.
