Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic
arXiv:2212.13499 · doi:10.1016/j.aim.2025.110153
Abstract
We prove the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic. This verifies a conjecture made by Rapoport and implies that the results of Nie and Zhou-Zhu can be extended to the whole irreducible components of affine Deligne-Lusztig varieties. The method is to translate the work of Hartl-Viehmann into mixed characteristic and construct local foliations for affine Deligne-Lusztig varieties. This leads us to develop a theory of formal algebraic geometry for perfect schemes.
18 pages; final version