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Supersingular Kottwitz–Rapoport strata and Deligne–Lusztig varieties

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry Abelian varieties and schemes

Published online by Cambridge University Press:  11 August 2009

Ulrich Görtz  and
Chia-Fu Yu
Ulrich Görtz
Affiliation:
Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany, ([email protected])
Chia-Fu Yu
Affiliation:
Institute of Mathematics, Academia Sinica, 128 Academia Road, Section 2, Nankang, Taipei, Taiwan and National Center for Theoretical Sciences (Taipei Office), National Taiwan University, Taipei 10617, Taiwan, ([email protected])
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Abstract

We investigate the special fibres of Siegel modular varieties with Iwahori level structure. On these spaces, we have the Newton stratification, and the Kottwitz–Rapoport (KR) stratification; one would like to understand how these stratifications are related to each other. We give a simple description of all KR strata which are entirely contained in the supersingular locus as disjoint unions of Deligne–Lusztig varieties. We also give an explicit numerical description of the KR stratification in terms of abelian varieties.

Keywords

Siegel modular varietiessupersingular locusIwahori level structureKottwitz–Rapoport strataDeligne–Lusztig varieties

MSC classification

Secondary: 14G35: Modular and Shimura varieties 14K10: Algebraic moduli, classification 11G18: Arithmetic aspects of modular and Shimura varieties
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 2 , April 2010 , pp. 357 - 390
Copyright
Copyright © Cambridge University Press 2010

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