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Non-invariance of the Hasse principle with Brauer–Manin obstruction

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Abstract

We study the Hasse principle with Brauer–Manin obstruction with respect to extensions of number fields. We give a general construction (conditional on a conjecture of M. Stoll) to prove that the failure of Hasse principle explained by the Brauer–Manin obstruction is not always invariant. Then we illustrate this construction with an explicit unconditional example.

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Acknowledgements

The author would like to thank his thesis advisor Y. Liang for proposing the related problems, papers and many fruitful discussions. We would like to express our heartfelt thanks to the anonymous referees for their careful scrutiny and valuable suggestions. The author was partially supported by NSFC Grant No. 12071448.

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  1. University of Science and Technology of China, School of Mathematical Sciences, No.96, JinZhai Road, Baohe District, 230026, Hefei, Anhui, People’s Republic of China

    Han Wu

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  1. Han Wu
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Wu, H. Non-invariance of the Hasse principle with Brauer–Manin obstruction. manuscripta math. 171, 457–471 (2023). https://doi.org/10.1007/s00229-022-01396-w

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  • DOI: https://doi.org/10.1007/s00229-022-01396-w

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