论文标题
hasse - witt矩阵和镜子复的铅笔
Hasse--Witt matrices and mirror toric pencils
论文作者
论文摘要
镜像表明，代数品种不同家族的算术特性之间的意外关系。例如，WAN和其他人表明，对于某些镜子对，有限字段上的理性点的数量与Modulo匹配该字段的顺序。在本文中，我们获得了某些镜像曲面的超曲面的相似结果。我们使用Huang，Lian，Yau和Yu的最新结果描述了这些品种的Picard-Fuchs方程与其Hasse-Witt矩阵之间的关系，这些矩阵封装了有关点数的信息。结果使我们能够明确计算点数的点数。我们通过计算与高几幅功能有关的K3表面示例来说明这一点。
Mirror symmetry suggests unexpected relationships between arithmetic properties of distinct families of algebraic varieties. For example, Wan and others have shown that for some mirror pairs, the number of rational points over a finite field matches modulo the order of the field. In this paper, we obtain a similar result for certain mirror pairs of toric hypersurfaces. We use recent results by Huang, Lian, Yau and Yu describing the relationship between the Picard-Fuchs equations of these varieties and their Hasse--Witt matrices, which encapsulate information about the number of points. The result allows us to compute the number of points modulo the order of the field explicitly. We illustrate this by computing K3 surface examples related to hypergeometric functions.
