Weak approximation on Ch\atelet surfaces
Abstract
We study weak approximation for Ch\atelet surfaces over number fields when all singular fibers are defined over rational points. We consider Ch\atelet 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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