On the Supersingular Locus of the $\mathrm{GU}(2,n-2)$ Shimura Variety
Ryosuke Shimada
TL;DR
This paper investigates the structure of the supersingular locus in a specific Shimura variety related to GU(2,n-2), revealing its decomposition into iterated fibrations over Deligne-Lusztig varieties after perfection.
Contribution
It provides a detailed geometric description of the supersingular locus for GU(2,n-2) Shimura varieties, including its decomposition into iterated fibrations over Deligne-Lusztig varieties.
Findings
Decomposition of the supersingular locus into disjoint unions.
Identification of the locus as iterated fibrations over Deligne-Lusztig varieties.
Results after taking perfection of the varieties.
Abstract
We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to . More concretely, we decompose the supersingular locus into a disjoint union of iterated fibrations over (classical) Deligne-Lusztig varieties after taking perfection.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Finite Group Theory Research · Algebraic Geometry and Number Theory