论文标题
在卡拉比（Calabi-yau
A transcendental Brauer-Manin obstruction to weak approximation on a Calabi-Yau threefold
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {q} $ - 简单连接的Calabi-yau三倍的$ \ Mathbb {q} $ - 最初是由Hosono和Takagi在镜面对称性的背景下研究的。这些品种被定义为双五五五重骨对称性的线性截面。他们的观点对应于对二次突出的裁决。他们配备了自然的$ 2 $ torsion brauer课程。我们的主要结果表明，在某些条件下，这种Brauer类会导致先验的Brauer-Manin障碍物迫使近似弱近似。 Hosono和Takagi表明，超过$ \ Mathbb {c} $这些calabi-yau三倍$ y $ $ y $的派生相当于reye的一致性calabi-yau三倍$ x $。我们表明，这些派生的等价也可以在$ \ mathbb {q} $上构造，并且我们为$ x $提供足够的条件，以不满足弱近似。在附录中，N。Addington在$ \ Mathbb {C} $上展示了每类Calabi-Yau品种的Brauer组。
In this paper we investigate the $\mathbb{Q}$-rational points of a class of simply connected Calabi-Yau threefolds, which were originally studied by Hosono and Takagi in the context of mirror symmetry. These varieties are defined as a linear section of a double quintic symmetroid; their points correspond to rulings on quadric hypersurfaces. They come equipped with a natural $2$-torsion Brauer class. Our main result shows that under certain conditions, this Brauer class gives rise to a transcendental Brauer-Manin obstruction to weak approximation. Hosono and Takagi showed that over $\mathbb{C}$ each of these Calabi-Yau threefolds $Y$ is derived equivalent to a Reye congruence Calabi-Yau threefold $X$. We show that these derived equivalences may also be constructed over $\mathbb{Q}$, and we give sufficient conditions for $X$ to not satisfy weak approximation. In the appendix, N. Addington exhibits the Brauer groups of each class of Calabi--Yau variety over $\mathbb{C}$.
