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

2005/09/03 by Inken Vollaard, Vollaard, Inken · 5 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.AG #math.NT #msc:11G18 #msc:14G35 #msc:14K10

paper · pdf · doi:10.48550/arxiv.math/0509067

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

arxiv created 2008/10/25 · arxiv updated 2009/12/01

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 equi-dimensional of dimension 1 and is of complete intersection. We give an explicit description of the irreducible components and their intersection behaviour.

Cited by

• The basic locus of regular ramified unitary Rapoport-Zink spaces at vertex-stabilizer level
• The basic locus of unitary splitting Rapoport-Zink spaces with vertex stabilizer level
• The Ekedahl-Oort and Newton stratification of the GU(3,2) Shimura variety
• Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups
• The cohomology of certain intermediate strata of Kottwitz varieties

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