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arXiv · 2410.05110

On the Supersingular Locus of the $\mathrm{GU}(2,n-2)$ Shimura Variety

Ryosuke Shimada
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Abstract

We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to $\mathrm{GU}(2,n-2)$. More concretely, we decompose the supersingular locus into a disjoint union of iterated fibrations over (classical) Deligne-Lusztig varieties after taking perfection. As an immediate application, when $p\geq3$, we prove an analogue of Oort's conjecture on the supersingular locus of the Siegel modular variety.

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Ryosuke Shimada. 2024-10-07. On the Supersingular Locus of the $\mathrm{GU}(2,n-2)$ Shimura Variety. https://arxiv.org/abs/2410.05110

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