Modularity of the Consani-Scholten quintic. With an appendix by José Burgos Gil and Ariel Pacetti

  • Luis Dieulefait

  • Ariel Pacetti

  • Matthias Schütt

Modularity of the Consani-Scholten quintic. With an appendix by José Burgos Gil and Ariel Pacetti cover
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Abstract

We prove that the Consani-Scholten quintic, a Calabi-Yau threefold over , 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 . We also need a Sturm bound for Hilbert modular forms; this is developed in an appendix by José Burgos Gil and the second author.

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Luis Dieulefait, Ariel Pacetti, Matthias Schütt, Modularity of the Consani-Scholten quintic. With an appendix by José Burgos Gil and Ariel Pacetti. Doc. Math. 17 (2012), pp. 953–987

DOI 10.4171/DM/386