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arXiv · 1301.0202

Local-global principle for certain biquadratic normic bundles

Yang Cao·Yongqi Liang
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Abstract

Let $X$ be a proper smooth variety having an affine open subset defined by the normic equation $N_{k(\sqrt{a},\sqrt{b})/k}({x})=Q(t_{1},...,t_{m})^{2}$ 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.

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Yang Cao, Yongqi Liang. 2013-01-02. Local-global principle for certain biquadratic normic bundles. https://arxiv.org/abs/1301.0202

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