The Ekedahl-Oort Stratification and the Semi-Module Stratification

TL;DR

This paper compares two stratifications of affine Deligne-Lusztig varieties, identifying when the semi-module stratification refines the Ekedahl-Oort stratification, revealing cases with simple geometric structures.

Contribution

It classifies when the semi-module stratification refines the Ekedahl-Oort stratification in the superbasic case, linking stratification refinement to geometric simplicity.

Findings

Semi-module stratification refines the Ekedahl-Oort stratification in certain cases.

Many cases with simple geometric structure are characterized by this refinement.

The classification applies specifically to the superbasic case.

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.