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

Published online by Cambridge University Press:  20 November 2018

Inken Vollaard
Inken Vollaard*
Affiliation:
Mathematisches Institut, Universität Bonn, Beringstr. 1, 53115 Bonn, Germany (Current address) c/o TorstenWedhorn, Institut fürMathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany, e-mail: ivollaard@gmx.de
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Abstract

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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.

Keywords

14G3511G1814K10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 3 , 01 June 2010 , pp. 668 - 720
Copyright
Copyright © Canadian Mathematical Society 2010

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