Arithmetic study of Calabi-Yau varieties with fibration

点击翻译按钮获取中文摘要

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.