论文标题
Brauer-Manin阻塞的弱近似弱近似的不变性
Non-invariance of weak approximation with Brauer--Manin obstruction
论文作者
论文摘要
在本文中，我们研究了brauer-曼宁障碍物的弱近似，相对于数量场的扩展。对于任何非平凡的扩展$ l/k，假设M. Stoll的猜想，我们证明存在$ k $ - threeflold，可以满足Brauer的弱近似值，而brauer-Manin阻塞了所有Archimedean的位置，而基本的基本变化为$ L $ $ $。然后，我们用明确的无条件示例来说明这种结构。
In this paper, we study weak approximation with Brauer--Manin obstruction with respect to extensions of number fields. For any nontrivial extension $L/K,$ assuming a conjecture of M. Stoll, we prove that there exists a $K$-threefold satisfying weak approximation with Brauer--Manin obstruction off all archimedean places, while its base change to $L$ fails. Then we illustrate this construction with an explicit unconditional example.
