Abstract
For rational points on algebraic varieties defined over a number field K, we study the behavior of the property of weak approximation with Brauer–Manin obstruction under extension of the ground field. We construct K-varieties accompanied with a quadratic extension such that the property holds over K (conditionally on a conjecture) whereas fails over L. The result is unconditional when K equals or certain quadratic number fields. We give an explicit example when .
Citation
Yongqi Liang. "Noninvariance of Weak Approximation Properties Under Extension of the Ground Field." Michigan Math. J. 73 (4) 675 - 692, August 2023. https://doi.org/10.1307/mmj/20205984
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