Deligne-Lusztig varieties and basic EKOR strata
Haining Wang
TL;DR
This paper explains how certain stratifications of Shimura varieties, specifically EKOR strata in basic loci, can be described as unions of Deligne-Lusztig varieties, connecting various descriptions in special cases.
Contribution
It clarifies the relationship between EKOR strata and Deligne-Lusztig varieties under He and Rapoport's axioms, and compares different descriptions in special cases.
Findings
EKOR strata in basic loci are disjoint unions of Deligne-Lusztig varieties.
Comparison of descriptions in Siegel modular varieties for various strata.
Connections between stratifications and Deligne-Lusztig theory established.
Abstract
Under the axiom of He and Rapoport for the stratifications of Shimura varieties, we explain a result of G\"{o}rtz, 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 Siegel modular varieties, we compare their descriptions to that of G\"{o}rtz and Yu for the supersingular Kottwitz-Rapoport strata and to the descriptions of Harashita, Hoeve for the supersingular Ekedahl-Oort strata.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Algebraic Geometry and Number Theory