Siegel modular forms mod p

Abstract

We prove a vanishing theorem for one forms on the moduli stack of principally polarized abelian varieties of genus g>1 with level structure N over fields of characteristic p different from two. This is used to compute the Picard groups of these stacks. As an application we obtain results one congruences between integral Siegel modular forms.

Cited by in corpus (1)

• Weights of the mod $p$ kernel of the theta operators