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Cohomology of the Bruhat-Tits strata in the supersingular locus of the $\mathrm{GU}(1,n-1)$ Shimura variety at a ramified prime
The supersingular locus of the $\mathrm{GU}(1,n-1)$ Shimura variety at a ramified prime $p$ is stratified by Coxeter varieties attached to finite symplectic groups. In this paper, we compute the $\ell$-adic cohomology of the Zariski closure of any such stratum. These are known as closed Bruhat-Tits strata. We prove that the …