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
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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.
DOI : 10.4171/dm/386
Classification : 11F41, 11F80, 11G40, 14G10, 14J32
Mots-clés : consani-scholten quintic, Hilbert modular form, faltings--Serre--livné method, Sturm bound 
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     author = {Luis Dieulefait and Ariel Pacetti and Matthias Sch\"utt},
     title = {Modularity of the {Consani-Scholten} quintic. {With} an appendix by {Jos\'e} {Burgos} {Gil} and {Ariel} {Pacetti}},
     journal = {Documenta mathematica},
     pages = {953--987},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/386},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/386/}
}
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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. Documenta mathematica, Tome 17 (2012), pp. 953-987. doi: 10.4171/dm/386

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