At arbitrary parahoric level, the reduced special fiber of the GU(1,n−1) Rapoport-Zink space is stratified by closures of fine Deligne-Lusztig varieties, with incidence controlled by Bruhat-Tits indices and n−m+1 J(E)-orbits of irreducible components.
On the Supersingular Locus of the $\mathrm{GU}(2,n-2)$ Shimura Variety
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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.
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The Bruhat-Tits stratification for basic unramified $GU(1,n-1)$ Rapoport-Zink spaces at arbitrary parahoric level
At arbitrary parahoric level, the reduced special fiber of the GU(1,n−1) Rapoport-Zink space is stratified by closures of fine Deligne-Lusztig varieties, with incidence controlled by Bruhat-Tits indices and n−m+1 J(E)-orbits of irreducible components.