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

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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Bibliographic Details
Published in:Science China. Mathematics 2023-04, Vol.66 (4), p.665-678
Main Author: Liang, Yongqi
Format: Article
Language:English
Subjects:
Applications of Mathematics
Approximation
Mathematical analysis
Mathematics
Mathematics and Statistics
Number theory
Citations: Items that this one cites
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Description
Summary: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-021-1994-0