The modularity conjecture for rigid Calabi-Yau threefolds over Q

2000/09/18 by Masa-Hiko Saito, Noriko Yui
Mathematics · #math.AG #math.NT #msc:14J32 #msc:11F11 #msc:11F80 #msc:11G18 #msc:14K30

paper · pdf

published as J. of Math. Kyoto Univ. 41-2 (2001), 403--419. · 16 pages, latex, minor corrections. references added

arxiv created 2000/09/18 · arxiv updated 2009/11/30

Abstract

We formulate the modularity conjecture for rigid Calabi-Yau threefolds defined over the field Q of rational numbers. We establish the modularity for the rigid Calabi-Yau threefold arising from the root lattice A₃. Our proof is based on geometric analysis.

Related

• Modularity of rigid Calabi-Yau threefolds over Q
• Rigid Calabi-Yau Threefolds over Q Are Modular
• On modularity of rigid and nonrigid Calabi-Yau varieties associated to the root lattice A₄
• On the modularity of rigid Calabi-Yau threefolds: Epilogue
• Update on Modular Non-Rigid Calabi-Yau Threefolds