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.
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.
@article{AIF_2004__54_3_666_0, author = {Moonen, Ben}, title = {A dimension formula for Ekedahl-Oort strata}, journal = {Annales de l'Institut Fourier}, volume = {54}, year = {2004}, pages = {666-698}, doi = {10.5802/aif.2029}, mrnumber = {2097418}, zbl = {1062.14033}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_2004__54_3_666_0} }
Moonen, Ben. A dimension formula for Ekedahl-Oort strata. Annales de l'Institut Fourier, Tome 54 (2004) pp. 666-698. doi : 10.5802/aif.2029. http://gdmltest.u-ga.fr/item/AIF_2004__54_3_666_0/
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