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arXiv · 2203.09156

Arithmetic of Chatelet surfaces under extensions of base fields

Han Wu
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Abstract

For Châtelet surfaces defined over number fields, we study two arithmetic properties, the Hasse principle and weak approximation, when passing to an extension of the base field. Generalizing a construction of Y. Liang, we show that for an arbitrary extension of number fields $L/K,$ there is a Châtelet surface over $K$ which does not satisfy weak approximation over any intermediate field of $L/K,$ and a Châtelet surface over $K$ which satisfies the Hasse principle over an intermediate field $L'$ if and only if $[L' : K]$ is even.

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Han Wu. 2022-03-17. Arithmetic of Chatelet surfaces under extensions of base fields. https://arxiv.org/abs/2203.09156

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