Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture

Harashita, Shushi

Annales de l'Institut Fourier, Tome 60 (2010) no. 5, pp. 1787-1830.

Nous étudions l’espace de modules de variétés abéliennes principalement polarisés en caractéristique positive. Dans cet article nous déterminons le polygone de Newton de tout point générique de chaque strate de Ekedahl-Oort, en prouvant la conjecture d’Oort sur les intersections de strates de polygone de Newton et de strates de Ekedahl-Oort. Ce résultat nous donne un algorithme combinatoire qui détermine la borne supérieure optimale des polygones de Newton de variétés abéliennes principalement polarisées avec un type de $p$-noyau donné .

We study the moduli space of principally polarized abelian varieties in positive characteristic. In this paper we determine the Newton polygon of any generic point of each Ekedahl-Oort stratum, by proving Oort’s conjecture on intersections of Newton polygon strata and Ekedahl-Oort strata. This result tells us a combinatorial algorithm determining the optimal upper bound of the Newton polygons of principally polarized abelian varieties with a given isomorphism type of $p$-kernel.

Classification : 14K10, 11G10, 14L05, 14L20
Keywords: Abelian varieties, the Newton polygon stratification, the Ekedahl-Oort stratification, Oort’s conjecture
Mot clés : variétés abéliennes, la stratification de polygone de Newton, la stratification de Ekedahl-Oort, la conjecture d’Oort

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