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Connected components of affine Deligne–Lusztig varieties in mixed characteristic

Published online by Cambridge University Press:  05 May 2015

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 [email protected]
Mark Kisin
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford St, Cambridge, MA 02138, USA email [email protected]
Eva Viehmann
Affiliation:
Fakultät für Mathematik der Technischen Universität München – M11, Boltzmannstr. 3, 85748 Garching, Germany email [email protected]
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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.

Type
Research Article
Copyright
© The Authors 2015 

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