On the Modularity of Three Calabi--Yau Threefolds With Bad Reduction at 11

Canadian mathematical bulletin

关键词: total positivity;    Toeplitz matrix;    Pólya frequency sequence;    skew Schur function;   

DOI  :  10.4153/CMB-2006-031-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

This paper investigates the modularity of threenon-rigid Calabi--Yau threefolds with bad reduction at 11. They areconstructed as fibre products of rational elliptic surfaces,involving the modular elliptic surface of level 5. Their middle$ell$-adic cohomology groups are shown to split intotwo-dimensional pieces, all but one of which can be interpreted interms of elliptic curves. The remaining pieces are associated tonewforms of weight 4 and level 22 or 55, respectively. For thispurpose, we develop a method by Serre to compare the correspondingtwo-dimensional 2-adic Galois representations with uneven trace.Eventually this method is also applied to a self fibre product ofthe Hesse-pencil, relating it to a newform of weight 4 and level27.

【 授权许可】

Unknown