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Flatness of the mod $p$ period morphism for the moduli space of principally polarized abelian varieties

Torsten Wedhorn
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Abstract

In this note it is shown that associating to a principally polarized abelian variety its de Rham cohomology defines a faithfully flat morphism of the moduli space of principally polarized abelian varieties in positive characteristics to the moduli space of symplectic $F$-Zips as defined in \cite{MW}.

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Torsten Wedhorn. 2005-07-08. Flatness of the mod $p$ period morphism for the moduli space of principally polarized abelian varieties. https://arxiv.org/abs/math/0507177

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