Irreducibility and \(p\)-adic monodromies on the Siegel moduli spaces
type: Item
instance of: scholarly article
title: Irreducibility and \(p\)-adic monodromies on the Siegel moduli spaces
zbMATH Open document ID: 1144.11048
author: Chia-Fu Yu
published in: Advances in Mathematics
publication date: 2008-06-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0612839
review text: The author studies Siegel modular varieties in positive characteristic \(p\) with parahoric level structure at \(p\). These are moduli spaces of chains of isogenies of abelian varieties of fixed dimension \(g\). In a previous paper [\textit{C.-F. Yu}, Int. Math. Res. Not. 2004, No. 48, 2593--2597 (2004; Zbl 1065.14059)] the author has determined the number of irreducible components in the case of Iwahori level structure. In the paper at hand, this question is considered for the non-ordinary locus, and for smaller strata, in the more general case of arbitrary parahoric level structure. The author gives explicit formulas for the number of irreducible components of the almost ordinary locus, and also for the number of connected components of arbitrary \(p\)-rank strata in these spaces. As in loc.~cit., an important ingredient is the theorem by Faltings and Chai about the surjectivity of the \(p\)-adic monodromy. In the final sections, the author discusses the case \(g=2\) with Iwahori level structure in detail, and in particular gives a very explicit geometric description of the supersingular locus and of the Kottwitz-Rapoport stratification.
reviewed by: Ulrich Görtz
Mathematics Subject Classification ID: 11G18
Mathematics Subject Classification ID: 14K10
zbMATH DE Number: 5285713
zbMATH Keywords: Siegel modular variety
zbMATH Keywords: \(p\)-adic monodromy
zbMATH Keywords: \(p\)-rank strata
MaRDI profile type: Publication
OpenAlex ID: W2073994398
arXiv ID: math/0612839
cites work: Q4277784
cites work: Lectures on \(p\)-divisible groups
cites work: Q3351514
cites work: On supersingular curves and Abelian varieties.
cites work: Q3997943
cites work: Q3409182
cites work: Q4359483
cites work: Q3775667
cites work: Q4097035
cites work: Minuscule alcoves for \(\text{GL}_n\) and \(\text{GSP}_{2n}\)
cites work: Moduli of supersingular abelian varieties
cites work: Alcoves and \(p\)-rank of abelian varieties
cites work: Moduli of abelian varieties
cites work: Q2739532
cites work: Period Spaces for "p"-divisible Groups (AM-141)
cites work: Siegel varieties and \(p\)-adic Siegel modular forms
cites work: Q4658954
cites work: The supersingular loci and mass formulas on Siegel modular varieties
DOI: 10.1016/J.AIM.2008.03.008
Recommended article: The \(p\)-rank stratification on the Siegel moduli space with Iwahori level structure
Recommended article: Kottwitz-Rapoport strata in the Siegel moduli spaces
Recommended article: Supersingular Kottwitz–Rapoport strata and Deligne–Lusztig varieties
Recommended article: On the reduction of the Siegel moduli space of abelian varieties of dimension 3 with Iwahori level structure
Recommended article: Alcoves and \(p\)-rank of abelian varieties
Recommended article: Normality and Cohen-Macaulayness of parahoric local models
Recommended article: Stratifying Lie strata of Hilbert modular varieties
Recommended article: Q4521512
Recommended article: Q4953653
Recommended article: Q5242679
description: scientific article