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Local-global principle for certain biquadratic normic bundles

Yang Cao, Yongqi Liang (2014)

Acta Arithmetica

Let X be a proper smooth variety having an affine open subset defined by the normic equation N k ( a , b ) / k ( x ) = Q ( t , . . . , t ) 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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