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Foliations in moduli spaces of abelian varieties

Frans Oort
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Abstract

Consider all moduli points corresponding with polarized abelian varieties in characteristic p such that the associated quasi-polarized p-divisible group is geometrically isomorphic with a given one. This defines a subset C of the moduli space. We show that C is closed in the corresponding open Newton polygon stratum. In this way the stratum is the disjoint union of such "central leaves". Under local-local isogenies we consider the orbit of one point: we obtain a second type of leaves. Every stratum, up to a finite map, is the product of one of its central leaves and one of its isogeny leaves. We expect that these central leaves describe Hecke actions prime to p.

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Frans Oort. 2007-01-17. Foliations in moduli spaces of abelian varieties. https://arxiv.org/abs/math/0207050

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