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

By Inken Vollaard. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2005

84 citations recorded by the source corpus.

Abstract 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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e76cbd8821e177f4db7ca0f149ad9ae421f073d4

How researchers see this paper

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In Discrete Mathematics and Combinatorics

1. Michael Rapoport
2. S. Kudla
3. T. Wedhorn
4. Inken Vollaard
5. W. Gan
6. Georgios Pappas

In Geometry and Topology

1. Michael Rapoport
2. S. Kudla
3. Inken Vollaard
4. T. Wedhorn
5. E. Viehmann
6. Xuhua He
7. Wei Zhang
8. Jan H. Bruinier

In Mathematical Physics

1. Michael Rapoport
2. S. Kudla
3. Inken Vollaard
4. T. Wedhorn
5. E. Viehmann
6. Xuhua He
7. Wei Zhang
8. Jan H. Bruinier

Citations in the corpus

• Special cycles on unitary Shimura varieties II: global theory (2009, background): “, to extend the results of [63], [65] and [39] to such primes.”
• The supersingular locus of the Shimura variety of GU(1,n−1) II (2008, methodology): “J .B y [ 14 ] Theorem 3.6 we have a natural identification of Bi (for fixed i) with B( ˜”
• Special cycles on unitary Shimura varieties I. Unramified local theory (2008, methodology): “There, the hope is expressed that such a relation should hold in greater generality for integral models of Shimura varieties attached to orthogonal groups of signature (2, n − 2) for any n.”
• The supersingular locus of the Shimura variety for GU(1,n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {GU} (2013, unknown): “Again we refer to the introduction of [28] for the precise references.”