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

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

2005-02-08

arxiv.org/abs/math/0502158v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

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.

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