math/0508127Aug 7, 200534 pages; To appear in "Mirror Symmetry V", Proceedings of the BIRS Workshop on Calabi-Yau Varieties and Mirror Symmetry, December 6-11, 2003. Some typos in tables corrected, proof of Lemma 5.6 corrected

A Modular Non-Rigid Calabi-Yau Threefold

Edward Lee

Algebraic Geometry Number Theory

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Abstract

We construct an algebraic variety by resolving singularities of a quintic Calabi-Yau threefold. The middle cohomology of the threefold is shown to contain a piece coming from a pair of elliptic surfaces. The resulting quotient is a two-dimensional Galois representation. By using the Lefschetz fixed-point theorem in étale cohomology and counting points on the variety over finite fields, this Galois representation is shown to be modular.

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