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arXiv · 2107.05205

Connectedness of affine Deligne-Lusztig varieties for unramified groups

Sian Nie
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Abstract

For unramified reductive groups, we determine the connected components of affine Deligne-Lusztig varieties in the partial affine flag varieties. Based on the 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 mod $p$ isogeny classes predicted by the Langlands-Rapoport conjecture, for the Kisin-Pappas integral models of Shimura varieties of Hodge type with parahoric level structure.

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Sian Nie. 2021-07-22. Connectedness of affine Deligne-Lusztig varieties for unramified groups. https://arxiv.org/abs/2107.05205

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