A dimension formula for Ekedahl-Oort strata
Annales de l'Institut Fourier, Volume 54 (2004) no. 3, p. 666-698
We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by the classes in a Weyl group modulo a subgroup, and each class has a distinguished representative of minimal length. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group element. We also discuss some explicit examples.
Nous étudions la stratification de Ekedahl-Oort sur les espaces de modules de type PEL. L'ensemble des strates est en correspondance avec les classes à droite d'un groupe de Weyl suivant un sous-groupe, et chaque classe a un élément distingué de longueur minimale. Le résultat principal de cet article est que la dimension d'une strate est égale à la longueur de l'élément du groupe de Weyl correspondant. Nous donnons quelques exemples explicites.
DOI : https://doi.org/10.5802/aif.2029
Classification:  14G35,  14L15,  11G15,  14K10,  14L05
Keywords: abelian varieties, Shimura varieties, finite group schemes, Dieudonné theory
@article{AIF_2004__54_3_666_0,
     author = {Moonen, Ben},
     title = {A dimension formula for Ekedahl-Oort strata},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {3},
     year = {2004},
     pages = {666-698},
     doi = {10.5802/aif.2029},
     zbl = {1062.14033},
     mrnumber = {2097418},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_3_666_0}
}
Moonen, Ben. A dimension formula for Ekedahl-Oort strata. Annales de l'Institut Fourier, Volume 54 (2004) no. 3, pp. 666-698. doi : 10.5802/aif.2029. http://www.numdam.org/item/AIF_2004__54_3_666_0/

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