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Connected components of affine Deligne–Lusztig varieties for unramified groups

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

Published online by Cambridge University Press:  17 August 2023

Sian Nie
Sian Nie*
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China niesian@amss.ac.cn School of Mathematical Sciences, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, PR China
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Abstract

For an unramified reductive group, we determine the connected components of affine Deligne–Lusztig varieties in the affine flag variety. Based on work of Hamacher, Kim, and Zhou, this result allows us to verify, in the unramified group case, the He–Rapoport axioms, the almost product structure of Newton strata, and the precise description of isogeny classes predicted by the Langlands–Rapoport conjecture, for the Kisin–Pappas integral models of Shimura varieties of Hodge type with parahoric level structure.

Keywords

affine Deligne–Lusztig varietiesconnected componentsreduction of Shimura varietiesLanglands–Rapoport conjecture

MSC classification

Primary: 20G25: Linear algebraic groups over local fields and their integers
Secondary: 14G35: Modular and Shimura varieties 11G18: Arithmetic aspects of modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 159 , Issue 10 , October 2023 , pp. 2051 - 2088
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Copyright
© 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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