Configuration of the central streams in the moduli of abelian varieties
type: Item
instance of: scholarly article
title: Configuration of the central streams in the moduli of abelian varieties
zbMATH Open document ID: 1193.14055
author: Shushi Harashita
published in: The Asian Journal of Mathematics
publication date: 2010-01-13T00:00:00Z
review text: 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.
reviewed by: Herbert Lange
Mathematics Subject Classification ID: 14K10
Mathematics Subject Classification ID: 11G10
Mathematics Subject Classification ID: 14L05
Mathematics Subject Classification ID: 14D20
zbMATH DE Number: 5657194
zbMATH Keywords: Newton polygon stratification
zbMATH Keywords: Ekedahl-Oort stratification
zbMATH Keywords: central streams
MaRDI profile type: Publication
DOI: 10.4310/AJM.2009.V13.N2.A4
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description: scientific article; zbMATH DE number 5657194