Connected components of affine Deligne-Lusztig varieties in mixed characteristic

Miaofen Chen; Mark Kisin; Eva Viehmann

doi:10.1112/S0010437X15007253

Connected components of affine Deligne-Lusztig varieties in mixed characteristic

Miaofen Chen
, Mark Kisin
, Eva Viehmann

Chair of Algorithmic Algebra

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1697-1762
Number of pages	66
Journal	Compositio Mathematica
Volume	151
Issue number	9
DOIs	https://doi.org/10.1112/S0010437X15007253
State	Published - 1 Sep 2015

Keywords

Rapoport-Zink space
affine Deligne-Lusztig variety
affine Grassmannian

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abstract = "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.",

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AU - Kisin, Mark

AU - Viehmann, Eva

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N2 - 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.

AB - 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.

KW - Rapoport-Zink space

KW - affine Deligne-Lusztig variety

KW - affine Grassmannian

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U2 - 10.1112/S0010437X15007253

DO - 10.1112/S0010437X15007253

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JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 9

ER -

Connected components of affine Deligne-Lusztig varieties in mixed characteristic

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Keywords

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