Modularity of the Consani-Scholten quintic
Number Theory
2012-12-13 v3 Algebraic Geometry
Abstract
We prove that the Consani-Scholten quintic, a Calabi-Yau threefold over QQ, is Hilbert modular. For this, we refine several techniques known from the context of modular forms. Most notably, we extend the Faltings-Serre-Livne method to induced four-dimensional Galois representations over QQ. We also need a Sturm bound for Hilbert modular forms; this is developed in an appendix by Jose Burgos Gil and the second author.
Keywords
Cite
@article{arxiv.1005.4523,
title = {Modularity of the Consani-Scholten quintic},
author = {Luis Dieulefait and Ariel Pacetti and Matthias Schuett},
journal= {arXiv preprint arXiv:1005.4523},
year = {2012}
}
Comments
35 pages, one figure; with an appendix by Jose Burgos Gil and Ariel Pacetti; v3: corrections and improvements thanks to the referee