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• W2951392570 abstract "The moduli space of (1,3) polarized abelian surfaces with full level-2 structure is birational to a double cover of the Barth-Nieto quintic. Barth and Nieto have shown that these varieties have Calabi-Yau models Z and Y , respectively. In this paper we apply the Weil conjectures to show that Y and Z are rigid and we prove that the L function of their common third étale cohomology group is modular, as predicted by a conjecture of Fontaine and Mazur. The corresponding modular form is the unique normalized cusp form of weight 4 for the group~ Γ 1 (6) . By Tate's conjecture, this should imply that Y , the fibred square of the universal elliptic curve~ S 1 (6) , and Verrill's rigid Calabi-Yau~ 𝒵 A 3 , which all have the same L function, are in correspondence over ℚ . We show that this is indeed the case by giving explicit maps." @default.
• W2951392570 created "2019-06-27" @default.
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• W2951392570 date "2001-08-16" @default.
• W2951392570 modified "2023-10-05" @default.
• W2951392570 title "The modularity of the Barth--Nieto quintic and its relatives" @default.
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• W2951392570 doi "https://doi.org/10.1515/advg.2001.017" @default.
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