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

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

2005-09-03

arxiv.org/abs/math/0509067v2

Mathematics

Number Theory

57 pages, LATEX, final version with minor changes, to appear in the Canadian Journal of Mathematics

Scientific paper

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.

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