论文标题
弱近似与Brauer-Manin障碍物的无变异性
Non-invariance of weak approximation with Brauer-Manin obstruction for surfaces
论文作者
论文摘要
在本文中，我们研究了数量场的场扩展，研究表面上具有Brauer-Manin障碍物的弱近似性能。对于M. Stoll的猜想，对于L/K的任何非平凡扩展，我们在K上构建了平滑，投影和几何连接的表面，以使其满足所有Archimedean位置的Brauer-Manin障碍物的弱近似，而其基本基本的基础变化为L失败。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 the property of weak approximation with Brauer-Manin obstruction for surfaces with respect to field extensions of number fields. For any nontrivial extension of number fields L/K, assuming a conjecture of M. Stoll, we construct a smooth, projective, and geometrically connected surface over K such that it satisfies 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.
