Dieulefait, Luis; Pacetti, Ariel; Schütt, Matthias [Burgos Gil, José] Modularity of the Consani-Scholten quintic. With an appendix by José Burgos Gil and Ariel Pacetti. (English) Zbl 1337.11029 Doc. Math. 17, 953-987 (2012). Summary: We prove that the Consani-Scholten quintic, a Calabi-Yau threefold over \(\mathbb Q\), 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 \(\mathbb Q\). We also need a Sturm bound for Hilbert modular forms; this is developed in an appendix by José Burgos Gil and the second author. Cited in 4 Documents MSC: 11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11F80 Galois representations 11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 14J32 Calabi-Yau manifolds (algebro-geometric aspects) Keywords:Consani-Scholten quintic; Hilbert modular form; Faltings-Serre-Livné method; Sturm bound Citations:Zbl 1115.14031 Software:PARI/GP PDFBibTeX XMLCite \textit{L. Dieulefait} et al., Doc. Math. 17, 953--987 (2012; Zbl 1337.11029) Full Text: arXiv EMIS