On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces

摘要

We prove that (not necessarily rigid) Calabi-Yau threefolds defined over therationals which contain sufficiently many elliptic ruled surfcaes are modular(under mild restrictions on the primes of bad reduction). Our proof uses theresults of Dieulefait and Manoharmayum who proved modularity of rigidCalabi-Yau threefolds.