We formulate the modularity conjecture for rigid Calabi-Yau threefolds defined over the field $\mathbf{Q}$ of rational numbers. We establish the modularity for the rigid Calabi-Yau threefold arising from the root lattice $A_{3}$. Our proof is based on geometric analysis.
Publié le : 2001-05-15
Classification:
11G40,
11F23,
11G35,
14G25,
14J32
@article{1250517640,
author = {Saito, Masa-Hiko and Yui, Noriko},
title = {The modularity conjecture for rigid Calabi-Yau threefolds over $\mathbf{Q}$},
journal = {J. Math. Kyoto Univ.},
volume = {41},
number = {4},
year = {2001},
pages = { 403-419},
language = {en},
url = {http://dml.mathdoc.fr/item/1250517640}
}
Saito, Masa-Hiko; Yui, Noriko. The modularity conjecture for rigid Calabi-Yau threefolds over $\mathbf{Q}$. J. Math. Kyoto Univ., Tome 41 (2001) no. 4, pp. 403-419. http://gdmltest.u-ga.fr/item/1250517640/