The Newton stratification on deformations of local G-shtukas

Abstract

Bounded local G-shtukas are function field analogs for p-divisible groups with extra structure. We describe their deformations and moduli spaces. The latter are analogous to Rapoport–Zink spaces for p-divisible groups. The underlying schemes of these moduli spaces are affine Deligne–Lusztig varieties. For basic Newton polygons the closed Newton stratum in the universal deformation of a local G-shtuka is isomorphic to the completion of a corresponding affine Deligne–Lusztig variety in that point. This yields bounds on the dimension and proves equidimensionality of the basic affine Deligne–Lusztig varieties.