Arithmetic and intermediate Jacobians of some rigid Calabi-Yau threefolds

Autor:	Molnar, Alexander
Rok vydání:	2015
Předmět:	Mathematics - Number Theory 11G40
Druh dokumentu:	Working Paper
Popis:	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. Comment: 20 pages. Many minor changes, including details added to numerous arguments, and typos fixed. Added examples using the CM automorphism, giving counterexamples, and added the CM cases to the higher dimension section
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1502.02778 Zobrazit plný text záznamu View this record from Arxiv