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Connected components of affine Deligne–Lusztig varieties in mixed characteristic

Part of: Arithmetic problems. Diophantine geometry Linear algebraic groups and related topics

Published online by Cambridge University Press:  05 May 2015

Miaofen Chen ,
Mark Kisin  and
Eva Viehmann
Miaofen Chen
Affiliation:
Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, No. 500, Dong Chuan Road, Shanghai, 200241, PR China email mfchen@math.ecnu.edu.cn
Mark Kisin
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford St, Cambridge, MA 02138, USA email kisin@math.harvard.edu
Eva Viehmann
Affiliation:
Fakultät für Mathematik der Technischen Universität München – M11, Boltzmannstr. 3, 85748 Garching, Germany email viehmann@ma.tum.de
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Abstract

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We determine the set of connected components of minuscule affine Deligne–Lusztig varieties for hyperspecial maximal compact subgroups of unramified connected reductive groups. Partial results are also obtained for non-minuscule closed affine Deligne–Lusztig varieties. We consider both the function field case and its analog in mixed characteristic. In particular, we determine the set of connected components of unramified Rapoport–Zink spaces.

Keywords

affine Deligne–Lusztig varietyaffine GrassmannianRapoport–Zink space

MSC classification

Primary: 14G35: Modular and Shimura varieties 20G25: Linear algebraic groups over local fields and their integers

Information

Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 9 , September 2015 , pp. 1697 - 1762
Copyright
© The Authors 2015 

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