Abstract
In this article, we establish the arithmetic purity of strong approximation for smooth loci of weighted projective spaces. By using this result and the descent method, we also prove that the arithmetic purity of strong approximation with Brauer–Manin obstruction holds for any smooth and complete toric variety.
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Acknowledgements
I thank Yang Cao for many fruitful discussions, and to Fei Xu and Yongqi Liang for many useful suggestions. I thank the referees for their careful scrutiny and valuable comments. The author is partially supported by National Natural Science Foundation of China No.12071448; Anhui Initiative in Quantum Information Technologies No. AHY150200; and Youth Innovation Fund of University of Science and Technology of China No. WK0010000078.
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Chen, S. Arithmetic purity of strong approximation for complete toric varieties. Math. Z. 306, 23 (2024). https://doi.org/10.1007/s00209-023-03418-z
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DOI: https://doi.org/10.1007/s00209-023-03418-z