zbMATH — the first resource for mathematics

Computing the level of a modular rigid Calabi-Yau threefold. (English) Zbl 1060.14059
Summary: In a previous article [L. Dieulefait and J. Manoharmayum, in: Calabi-Yau varieties and mirror symmetry. Fields Inst. Commun. 38, 159–166 (2003; Zbl 1096.14015)] the modularity of a large class of rigid Calabi-Yau threefolds was established. To make that result more explicit, we recall (and reprove) a result of Serre giving a bound for the conductor of “integral” two-dimensional compatible families of Galois representations and apply this result to give an algorithm that determines the level of a modular rigid Calabi-Yau threefold. We apply the algorithm to three examples.

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
11F23 Relations with algebraic geometry and topology
11F80 Galois representations
Full Text: DOI Euclid EuDML arXiv
[1] DOI: 10.1090/S0894-0347-01-00370-8 · Zbl 0982.11033
[2] DOI: 10.1215/S0012-7094-89-05937-1 · Zbl 0703.11027
[3] Dieulefait L., Calabi-Yau Varieties and Mirror Symmetry (2003)
[4] DOI: 10.1215/S0012-7094-87-05413-5 · Zbl 0641.10026
[5] DOI: 10.1007/978-1-4612-0851-8
[6] Stein W., ”The Modular Forms Explorer.” (2000)
[7] Taylor R., ”On the Meromorphic Continuation of Degree Two L-Functions.” (2001)
[8] Yui N., Calabi-Yau Varieties and Mirror Symmetry (2003) · Zbl 1022.00014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.