Geodesic
On the Modularity of Three Calabi–Yau Threefolds With Bad Reduction at 11
Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 296-312

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DOI

This paper investigates the modularity of three non-rigid Calabi–Yau threefolds with bad reduction at 11. They are constructed as fibre products of rational elliptic surfaces, involving the modular elliptic surface of level 5. Their middle $\ell$ -adic cohomology groups are shown to split into two-dimensional pieces, all but one of which can be interpreted in terms of elliptic curves. The remaining pieces are associated to newforms of weight 4 and level 22 or 55, respectively. For this purpose, we develop a method by Serre to compare the corresponding two-dimensional 2-adic Galois representations with uneven trace. Eventually this method is also applied to a self fibre product of the Hesse-pencil, relating it to a newform of weight 4 and level 27.
DOI : 10.4153/CMB-2006-031-9
Mots-clés : 14J32, 11F11, 11F23, 20C12 
Schütt, Matthias. On the Modularity of Three Calabi–Yau Threefolds With Bad Reduction at 11. Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 296-312. doi: 10.4153/CMB-2006-031-9
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     title = {On the {Modularity} of {Three} {Calabi{\textendash}Yau} {Threefolds} {With} {Bad} {Reduction} at 11},
     journal = {Canadian mathematical bulletin},
     pages = {296--312},
     year = {2006},
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     doi = {10.4153/CMB-2006-031-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-031-9/}
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