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arXiv · 2106.10643

Arithmetic of Ch\^atelet surface bundles revisited

Guang Hu·Yongqi Liang
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Abstract

We study arithmetic of the algebraic varieties defined over number fields by applying Lagrange interpolation to fibrations. Assuming the finiteness of the Tate-Shafarevich group of a certain elliptic curve, we show, for Ch\^atelet surface bundles over curves, that the violation of Hasse principle being accounted for by the Brauer-Manin obstruction is not invariant under an arbitrary finite extension of the ground field.

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Guang Hu, Yongqi Liang. 2021-06-20. Arithmetic of Ch\^atelet surface bundles revisited. https://arxiv.org/abs/2106.10643

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