Connectedness of affine Deligne-Lusztig varieties for unramified groups

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.

25 pages

References in corpus (3)

• A guide to the reduction modulo p of Shimura varieties
• Minimal length elements in conjugacy classes of extended affine Weyl group
• EKOR strata for Shimura varieties with parahoric level structure

Cited by in corpus (1)

• Mod $p$ points on Shimura varieties of parahoric level (with an appendix by Rong Zhou)