In this paper we study the supersingular locus of the reduction modulo $p$ of the Shimura variety for $GU(1,s)$ in the case of an inert prime $p$. Using Dieudonné theory we define a stratification of the corresponding moduli space of $p$-divisible groups. We describe the incidence relation of this stratification in terms of the Bruhat--Tits building of a unitary group. In the case of $GU(1,2)$, we show that the supersingular locus is equidimensional of dimension 1 and is of complete intersection. We give an explicit description of the irreducible components and their intersection behaviour.

MSC Classifications:

14G35, 11G18, 14K10 show english descriptions Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
Arithmetic aspects of modular and Shimura varieties [See also 14G35]
Algebraic moduli, classification [See also 11G15] 14G35 - Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
11G18 - Arithmetic aspects of modular and Shimura varieties [See also 14G35]
14K10 - Algebraic moduli, classification [See also 11G15]

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