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The supersingular locus of the Shimura variety for GU(1,s)

Inken Vollaard
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Abstract

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 equi-dimensional of dimension 1 and is of complete intersection. We give an explicit description of the irreducible components and their intersection behaviour.

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Inken Vollaard. 2008-10-25. The supersingular locus of the Shimura variety for GU(1,s). https://arxiv.org/abs/math/0509067

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