The Supersingular Locus of the Shimura Variety for GU(1, s)

Vollaard, Inken

Canadian journal of mathematics, Tome 62 (2010) no. 3, pp. 668-720

Résumé

In this paper we study the supersingular locus of the reduction modulo $p$ of the Shimura variety for $\text{GU}\left( 1,\,s \right)$ 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 $\text{GU}\left( 1,\,2 \right)$ , 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.

Détail

DOI : 10.4153/CJM-2010-031-2

Mots-clés : 14G35, 11G18, 14K10

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