The Ekedahl–Oort stratification and the semi-module stratification

Abstract In this paper, we compare the $\mathbb J$ -stratification (or the semi-module stratification) and the Ekedahl–Oort stratification of affine Deligne–Lusztig varieties in the superbasic case. In particular, we classify the cases where the $\mathbb J$ -stratification gives a refinement of the Ekedahl–Oort stratification, which include many interesting cases such that the affine Deligne-Lusztig variety admits a simple geometric structure.