Equivalued affine springer fibers in mixed characteristic

We study Witt-vector affine Springer fibers for tame equi-valued conjugacy classes in tamely ramified groups.

Similar to the approach of Goresky-Kottwitz-MacPherson in the equal characteristic setting, we show that they admit pavings by perfections of iterated affine space bundles over smooth Hessenberg varieties.

Along the way we prove a version of the Chevalley restriction theorem for the dual of Lie algebras.