Modularity of the Consani-Scholten quintic

Details Modularity of the Consani-Scholten quintic Modularity of the Consani-Scholten quintic

2010-05-25

arxiv.org/abs/1005.4523v2

Mathematics

Number Theory

29 pages, one figure; with an appendix by Jose Burgos Gil and Ariel Pacetti; v2 introduces a quadratic twist of the Hilbert mo

Scientific paper

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 developped in an appendix by Jose Burgos Gil and the second author.

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