Abstract
The moduli space of principally polarized abelian varieties of dimensiongadmits in positive characteristicpa stratification by the p-rank of the abelian variety, i.e. by the rank of the p-torsion. In the case of the moduli space of elliptic curves this is simply the stratification given by the (open and dense) ordinary locus and the zero-dimensional supersingular locus. But forg >2 this stratification is too coarse for many purposes. A refinement is provided by stratifying the moduli space according to the Newton polygon of an abelian variety. This stratification has been studied thoroughly by Oort ([OO1], [Oo2], see also [dJO]). He also suggested to study another stratification given by the isomorphism type of the p-torsion which we will call the Oort stratification in the sequel (often it is also called Ekedahl-Oort stratification). This stratification is also a refinement of the p-rank stratification.
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Wedhorn, T. (2001). The Dimension of Oort Strata of Shimura Varieties of Pel-Type. In: Faber, C., van der Geer, G., Oort, F. (eds) Moduli of Abelian Varieties. Progress in Mathematics, vol 195. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8303-0_15
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DOI: https://doi.org/10.1007/978-3-0348-8303-0_15
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