Abstract
We study weak approximation for Châtelet surfaces over number fields when all singular fibers are defined over rational points. We consider Châtelet 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-Thélène, Sansuc, and Swinnerton-Dyer.
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Acknowledgements
We are grateful to Bianca Viray for helpful discussions and comments. We also thank Daniel Loughran, Jean-Louis Colliot-Thélène for comments on the initial draft of the paper. Finally, we thank the referee for all their comments and suggestions.
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Nakahara, M., Roven, S. Weak approximation on Châtelet surfaces. manuscripta math. (2024). https://doi.org/10.1007/s00229-024-01548-0
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DOI: https://doi.org/10.1007/s00229-024-01548-0