TY - JOUR

T1 - On the modularity of three Calabi-Yau threefolds with bad reduction at 11

AU - Schütt, Matthias

PY - 2006/6

Y1 - 2006/6

N2 - 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 ℓ-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.

AB - 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 ℓ-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.

UR - http://www.scopus.com/inward/record.url?scp=33745258402&partnerID=8YFLogxK

UR - https://arxiv.org/pdf/math/0405450.pdf

U2 - 10.4153/CMB-2006-031-9

DO - 10.4153/CMB-2006-031-9

M3 - Article

AN - SCOPUS:33745258402

VL - 49

SP - 296

EP - 312

JO - Canadian mathematical bulletin

JF - Canadian mathematical bulletin

SN - 0008-4395

IS - 2

ER -