2010/05/25 by Luís Dieulefait, Luis Dieulefait, Dieulefait, Luis +5 · 1 citation
Mathematics · #11F41 (Primary) 11F80 #11G40 #14G10 #14J32 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.AG #math.NT #msc:11F41 #msc:11F80 #msc:11G40 #msc:14G10 #msc:14J32
paper · pdf · doi:10.48550/arxiv.1005.4523
35 pages, one figure; with an appendix by Jose Burgos Gil and Ariel Pacetti; v3: corrections and improvements thanks to the referee
openalex publication_date 2010/05/25 · arxiv created 2012/12/12 · arxiv updated 2012/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 developed in an appendix by Jose Burgos Gil and the second author.