Arithmetic study of Calabi-Yau varieties with fibration

利用椭圆曲线和（或）K3曲面研究了带纤裂的Calabi-Yau三倍体的算法。重点讨论了在数域上的加权投影空间中定义的Delsarte型Calabi-Yau三倍，以及Voisin和Borcea在构造镜像对称时所考虑的Calabi-Yau三倍。考虑到振动的信息，我们计算了这类Calabi-Yau三重函数的上同调、zeta函数和l函数。此外，我们还得到了它们的模性（自同构）和形式群的高度的结果。

We studied the arithmetic of Calabi-Yau threefolds with fibration by elliptic curves and/or K3 surfaces. The focus was put on Calabi-Yau threefolds of Delsarte type defined in a weighted projective space over a number field and also on Calabi-Yau threefolds considered by Voisin and Borcea in their construction of mirror symmetry. Taking into account the information of fibrations, we computed the cohomology, zeta functions and L-functions of such Calabi-Yau threefolds. We moreover obtained results on their modularity (automorphy) and on the height of their formal groups.