Geodesic
Modularity of the Consani-Scholten quintic. With an appendix by José Burgos Gil and Ariel Pacetti
Documenta mathematica, Tome 17 (2012), pp. 953-987.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We prove that the Consani-Scholten quintic, a Calabi-Yau threefold over $\Q$, is Hilbert modular. For this, we refine several techniques known from the context of modular forms. Most notably, we extend the Faltings-Serre-Livné method to induced four-dimensional Galois representations over $\Q$. We also need a Sturm bound for Hilbert modular forms; this is developed in an appendix by José Burgos Gil and the second author.
Classification : 11F41, 11F80, 11G40, 14G10, 14J32
Keywords: consani-scholten quintic, Hilbert modular form, faltings--Serre--livné method, Sturm bound 
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     title = {Modularity of the {Consani-Scholten} quintic. {With} an appendix by {Jos\'e} {Burgos} {Gil} and {Ariel} {Pacetti}},
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Dieulefait, Luis; Pacetti, Ariel; Schütt, Matthias. Modularity of the Consani-Scholten quintic. With an appendix by José Burgos Gil and Ariel Pacetti. Documenta mathematica, Tome 17 (2012), pp. 953-987. http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a2/