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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Affine Deligne-Lusztig varieties and the action of $ J$


Authors: Miaofen Chen and Eva Viehmann
Journal: J. Algebraic Geom. 27 (2018), 273-304
DOI: https://doi.org/10.1090/jag/693
Published electronically: September 29, 2017
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Abstract | References | Additional Information

Abstract: We propose a new stratification of the reduced subschemes of Rapoport-Zink spaces and of affine Deligne-Lusztig varieties that highlights the relation between the geometry of these spaces and the action of the associated automorphism group. We show that this provides a joint group-theoretic interpretation of well-known stratifications which only exist for special cases such as the Bruhat-Tits stratification of Vollaard and Wedhorn, the semi-module stratification of de Jong and Oort, and the locus where the $ a$-invariant is equal to $ 1$.


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Additional Information

Miaofen Chen
Affiliation: Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, No. 500, Dong Chuan Road, Shanghai, 200241, People’s Republic of China
Email: mfchen@math.ecnu.edu.cn

Eva Viehmann
Affiliation: Technische Universität München, Zentrum Mathematik – M11, Boltzmannstr. 3, 85748 Garching, Germany
Email: viehmann@ma.tum.de

DOI: https://doi.org/10.1090/jag/693
Received by editor(s): November 25, 2015
Received by editor(s) in revised form: May 2, 2016
Published electronically: September 29, 2017
Additional Notes: The first author was partially supported by NSFC grant No. 11301185, SRFDP grant No. 20130076120002, and STCSM grant No. 13dz2260400. The second author was partially supported by ERC starting grant 277889 “Moduli spaces of local $G$-shtukas”.
Article copyright: © Copyright 2017 University Press, Inc.

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