The supersingular locus of the Shimura variety for GU(1,s)
Number Theory
2008-10-25 v2 Algebraic Geometry
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 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.
Keywords
Cite
@article{arxiv.math/0509067,
title = {The supersingular locus of the Shimura variety for GU(1,s)},
author = {Inken Vollaard},
journal= {arXiv preprint arXiv:math/0509067},
year = {2008}
}
Comments
57 pages, LATEX, final version with minor changes, to appear in the Canadian Journal of Mathematics