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

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

2004-05-24

arxiv.org/abs/math/0405450v2

Canad. Math. Bull. 49 (2), 2006, 296-312

Mathematics

Algebraic Geometry

15 pages; minor changes and corrections to first version; accepted for Canadian Mathematical Bulletin

Scientific paper

We investigate the modularity of three non-rigid Calabi-Yau threefolds with bad reduction at 11 which arise as fibre products of rational elliptic surfaces. For this purpose, we apply a method by Serre to compare two-dimensional 2-adic Galois representations with uneven trace. Hereby, we associate two of the threefolds (or, more precisely, a two-dimensional piece of their middle cohomology group) to newforms of weight 4 and level 22 and 55, respectively. This enables us to compute the zeta-functions of these varieties up to the Euler factors of the bad primes.

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