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

Abstract

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

17 pages

References in corpus (2)

• Modularity of rigid Calabi-Yau threefolds over Q
• From potential modularity to modularity for integral Galois representations and rigid Calabi-Yau threefolds

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