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arXiv · 1210.4190

Towards the Brauer-Manin obstruction on varieties fibred over the projective line

Yongqi Liang
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Abstract

Recently Dasheng Wei proved that the Brauer-Manin obstruction is the only obstruction to the Hasse principle for 0-cycles of degree 1 on some fibrations over the projective line defined by bi-cyclic normic equations. In the present paper, we prove the exactness of the global-to-local sequence for Chow groups of 0-cycles of such varieties, which signifies that the Brauer-Manin obstruction is also the only obstruction to weak approximation for 0-cycles of arbitrary degree. Our main theorem also generalizes several existing results.

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Yongqi Liang. 2012-10-15. Towards the Brauer-Manin obstruction on varieties fibred over the projective line. https://arxiv.org/abs/1210.4190

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