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arXiv · 0711.0239

Superspecial Abelian Varieties and the Eichler Basis Problem for Hilbert Modular Forms

Marc-Hubert Nicole
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Abstract

Let $p$ be an unramified prime in a totally real field $L$ such that $h^+(L)=1$. Our main result shows that Hilbert modular newforms of parallel weight two for $Γ_0(p)$ can be constructed naturally, via classical theta series, from modules of isogenies of superspecial abelian varieties with real multiplication on a Hilbert moduli space. This can be viewed as a geometric reinterpretation of the Eichler Basis Problem for Hilbert modular forms.

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BibTeXRIS

Marc-Hubert Nicole. 2008-06-17. Superspecial Abelian Varieties and the Eichler Basis Problem for Hilbert Modular Forms. https://doi.org/10.1016/j.jnt.2008.01.006

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