Deligne-Lusztig varieties and basic EKOR strata

Using the axioms of He and Rapoport for the stratifications of Shimura varieties, we explain a result of Gortz, He, and Nie that the EKOR strata contained in the basic loci can be described as a disjoint union of Deligne-Lusztig varieties. In the special case of Siegelmodular varieties, we compare their descriptions to that of Gortz and Yu for the supersingular Kottwitz-Rapoport strata and to the descriptions of Harashita and Hoeve for the supersingular Ekedahl-Oort strata.

Automated summary

This paper explains the stratifications of Shimura varieties using the axioms of He and Rapoport, and discusses a result by Gortz, He, and Nie that the EKOR strata within the basic loci can be described as a disjoint union of Deligne-Lusztig varieties. In the special case of Siegelmodular varieties, comparisons are made with descriptions by Gortz and Yu for supersingular Kottwitz-Rapoport strata, as well as descriptions by Harashita and Hoeve for supersingular Ekedahl-Oort strata.