论文标题
Brauer-Manin障碍物的Châtelet表面和不变性，价格为3美元
Châtelet surfaces and non-invariance of the Brauer-Manin obstruction for $3$-folds
论文作者
论文摘要
在本文中，我们构造了三种形式的布尔孔表面，它们在数字场的场扩展方面具有一些给定的算术特性。然后，我们使用这些结构来研究弱近似值的特性，并以brauer-manin障碍物和带有brauer-manin障碍物的Hasse原理，价格为$ 3 $ folds，它们是通过曲线参数式的曲线铅笔，与曲线相对于场扩展字段的数字场。我们给出一般的构造（以M. Stoll的猜想为条件），以负回答一些问题，并用一些明确的无条件示例说明了这些构造和一些例外。
In this paper, we construct three kinds of Châtelet surfaces, which have some given arithmetic properties with respect to field extensions of number fields. We then use these constructions to study the properties of weak approximation with Brauer-Manin obstruction and the Hasse principle with Brauer-Manin obstruction for $3$-folds, which are pencils of Châtelet surfaces parameterized by a curve, with respect to field extensions of number fields. We give general constructions (conditional on a conjecture of M. Stoll) to negatively answer some questions, and illustrate these constructions and some exceptions with some explicit unconditional examples.
