On the modularity of three Calabi-Yau threefolds with bad reduction at 11
Algebraic Geometry
2007-05-23 v2 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/0405450,
title = {On the modularity of three Calabi-Yau threefolds with bad reduction at 11},
author = {Matthias Schuett},
journal= {arXiv preprint arXiv:math/0405450},
year = {2007}
}
Comments
15 pages; minor changes and corrections to first version; accepted for Canadian Mathematical Bulletin