Inken Vollaard
Published 2005-09-03, updated 2008-10-25Version 2
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 Dieudonn\'e 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.
Comments: 57 pages, LATEX, final version with minor changes, to appear in the Canadian Journal of Mathematics
Ekedahl-Oort strata and the supersingular locus in the GU(q-2,2) Shimura variety
The supersingular locus of the Shimura variety of $\mathrm{GU}(2,n-2)$
On the characterization of complex Shimura varieties
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