Modularity of rigid Calabi-Yau threefolds over Q

Abstract

We prove modularity for a huge class of rigid Calabi-Yau threefolds over $\Q$. In particular we prove that every rigid Calabi-Yau threefold with good reduction at 3 and 7 is modular.

to appear at: Proceedings of the Workshop on "Calabi-Yau Varieties and Mirror Symmetry", Fields Institute, Toronto, July 23-29, 2001 ; Fields Inst. Comm. Series, AMS

Cited by in corpus (12)

• On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces
• New realizations of modular forms in Calabi-Yau threefolds arising from ${\varphi }^4$ theory
• Remarks on Serre's modularity conjecture
• On modularity of rigid and nonrigid Calabi-Yau varieties associated to the root lattice A_4
• How to facet a gemstone: from potential modularity to the proof of Serre's modularity conjecture
• From potential modularity to modularity for integral Galois representations and rigid Calabi-Yau threefolds
• New examples of modular rigid Calabi-Yau threefolds
• On the modularity of three Calabi-Yau threefolds with bad reduction at 11
• Modularity of some non-rigid double octic Calabi-Yau threefolds
• The level 1 weight 2 case of Serre's conjecture
• Computing the level of a modular rigid Calabi-Yau threefold
• On the modularity of rigid Calabi-Yau threefolds: Epilogue