Connected components of affine Deligne-Lusztig varieties in mixed characteristic

Abstract

We determine the set of connected components of minuscule affine Deligne-Lusztig varieties for special 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.

69 pages, v2: final version. Numerous modifications to improve readability, and minor corrections. The main results are unchanged

References in corpus (3)

• On parahoric subgroups
• On the Hodge-Newton decomposition for split groups
• On the Hodge-Newton filtration for p-divisible O-modules

Cited by in corpus (20)

• Towards a theory of local Shimura varieties
• Rapoport-Zink spaces for spinor groups
• Fully Hodge-Newton decomposable Shimura varieties
• On the connected components of affine Deligne-Lusztig varieties
• Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties
• The geometry of Newton strata in the reduction modulo $p$ of Shimura varieties of PEL type
• Irreducible components of minuscule affine Deligne-Lusztig varieties
• Affine Grassmannians and the geometric Satake in mixed characteristic
• Mod-$p$ isogeny classes on Shimura varieties with parahoric level structure
• On some generalized Rapoport-Zink spaces
• The dimension of affine Deligne-Lusztig varieties in the affine Grassmannian of unramified groups
• Serre-Tate theory for Shimura varieties of Hodge type
• Affine Deligne-Lusztig varieties and the action of J
• Monodromy and Irreducibility of Igusa Varieties
• Eichler-Shimura Relations for Shimura Varieties of Hodge Type
• Connectedness of affine Deligne-Lusztig varieties for unramified groups
• The connected components of affine Deligne--Lusztig varieties
• Connected components of closed affine Deligne-Lusztig varieties
• The plectic conjecture over local fields
• Mod $p$ points on Shimura varieties of parahoric level (with an appendix by Rong Zhou)