The Ekedahl-Oort Stratification and the Semi-Module Stratification

Author:

Ryosuke Shimada

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Number Theory (math.NT), Representation Theory (math.RT)

journal:

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date:

2023-09-05 16:00:00

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.