论文标题
横幅曲线的Brauer-Manin障碍物
The Brauer-Manin obstruction for stacky curves
论文作者
论文摘要
我们表明，Brauer-Manin障碍物是具有有限的Abelian基本组的全球田野上所有堆叠曲线的唯一障碍。这包括属$ g = \ frac {1} {2} $的所有二叠纪曲线，从而解释了Bhargava-Poonen的Hasse原理的最新反例。我们还将表明，基本障碍是整体hasse原理的唯一障碍物，即平滑的$ g <1 $的二叠纪曲线的合适积分模型。然后，我们计算Brauer-manin障碍物，以使属$ \ frac {1} {2} $的二叠纪曲线的正确积分模型平滑。
We show that the Brauer-Manin obstruction is the only obstruction to strong approximation for all stacky curves over global fields with finite abelian fundamental groups. This includes all stacky curves of genus $g = \frac{1}{2}$, thus explaining a recent counterexample to the Hasse principle of Bhargava-Poonen. We will furthermore show that the elementary obstruction is the only obstruction to the integral Hasse principle for smooth proper integral models of stacky curves of genus $g < 1$. We then compute the Brauer-Manin obstruction for smooth proper integral models of stacky curves of genus $\frac{1}{2}$.
