Configuration of the central streams in the moduli of abelian varieties
Let \({\mathcal A}_g\) denote the moduli space of principally polarized abelian varieties (ppav) of dimension \(g\) in characterisic \(p> 0\). There are two important stratifications of \({\mathcal A}_g\), one by symmetric Newton polygons and the other, called Ekedahl-Oort stratification, by the type of the \(p\)-kernel \(X[p]\) of a ppav \(X\in{\mathcal A}_g\). The central stream of a Newton polygon \(\xi\) is the subspace of \({\mathcal A}_g\) with Newton polygon \(\xi\) whose geometric fibres have minimal \(p\)-divisible group. The main result of the paper is determination of the configuration of the central streams in \({\mathcal A}_g\). This uses the fact that the central stream is the Ekedahl-Oort stratum for a certain elementary sequence. From this a proof of the dimension formula of the central streams is deduced (which originally is due to \textit{F. Oort} [in: Automorphic forms (I). Proceedings of the Semester of the Emile Borel Center, Paris, France, February 17--July 11, 2000. Paris: SMF. Astérisque 298, 255--269 (2005; Zbl 1078.14063)]. Another consequence is a contribution to Oorts conjecture on the intersections of Newton polygon strata and Ekedahl-Oort strata.
scientific article; zbMATH DE number 5657194
scientific article