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Compatibility of weak approximation for zero-cycles on products of varieties

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Abstract

The Brauer-Manin obstruction is conjectured to be the only obstruction to weak approximation for zero-cycles on proper smooth varieties defined over number fields. We prove that the conjecture is compatible for products of rationally connected varieties, K3 surfaces, Kummer varieties and one curve.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 12071448) and Anhui Initiative in Quantum Information Technologies (Grant No. AHY150200). The author thanks the referees for their very detailed comments and helpful suggestions.

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  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Yongqi Liang

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Liang, Y. Compatibility of weak approximation for zero-cycles on products of varieties. Sci. China Math. 66, 665–678 (2023). https://doi.org/10.1007/s11425-021-1994-0

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  • DOI: https://doi.org/10.1007/s11425-021-1994-0

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