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

Published:2010-01-26
Printed: Jun 2010
• Inken Vollaard,
Mathematisches Institut, Universität Bonn, Beringstr. 1, 53115 Bonn, Germany
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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 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 - 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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