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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170555Let $p$ 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.to appear in J.N.TNumber TheoryAlgebraic Geometry11G10; 11G18; 11F27; 11F41;14G35.Superspecial Abelian Varieties and the Eichler Basis Problem for Hilbert Modular Formstext