Weak approximation on Ch\^{a}telet surfaces

Masahiro Nakahara; Samuel Roven

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arXiv · 2206.10556

Weak approximation on Ch\^{a}telet surfaces

Masahiro Nakahara·Samuel Roven

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Abstract

We study weak approximation for Ch\^{a}telet surfaces over number fields when all singular fibers are defined over rational points. We consider Ch\^{a}telet surfaces which satisfy weak approximation over every finite extension of the ground field. We prove many of these results by showing that the Brauer-Manin obstruction vanishes, then apply results of Colliot-Th\'el\`ene, Sansuc, and Swinnerton-Dyer.

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Masahiro Nakahara, Samuel Roven. 2022-06-21. Weak approximation on Ch\^{a}telet surfaces. https://arxiv.org/abs/2206.10556

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