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arXiv · 1502.02778

Arithmetic and intermediate Jacobians of some rigid Calabi-Yau threefolds

Alexander Molnar
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Abstract

We construct Calabi-Yau threefolds defined over $\mathbb{Q}$ via quotients of abelian threefolds, and re-verify the rigid Calabi-Yau threefolds in this construction are modular by computing their L-series, without \cite{Dieulefait} or \cite{GouveaYui}. We compute the intermediate Jacobians of the rigid Calabi-Yau threefolds as complex tori, then compute a $\mathbb{Q}$-model for the 1-torus given a $\mathbb{Q}$-structure on the rigid Calabi-Yau threefolds, and find infinitely many examples and counterexamples for a conjecture of Yui about the relation between the $L$-series of the rigid Calabi-Yau threefolds and the $L$-series of their intermediate Jacobians.

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Alexander Molnar. 2015-06-12. Arithmetic and intermediate Jacobians of some rigid Calabi-Yau threefolds. https://arxiv.org/abs/1502.02778

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