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A Modular Non-Rigid Calabi-Yau Threefold

Edward Lee
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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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Edward Lee. 2005-10-27. A Modular Non-Rigid Calabi-Yau Threefold. https://arxiv.org/abs/math/0508127

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