The Newton stratification on deformations of local G-shtukas

TL;DR

This paper studies the deformation theory and moduli spaces of bounded local G-shtukas, revealing their structure as affine Deligne-Lusztig varieties and establishing properties like dimension bounds and equidimensionality.

Contribution

It provides a detailed description of the deformation spaces of local G-shtukas and links their Newton stratification to affine Deligne-Lusztig varieties, extending understanding in the function field setting.

Findings

The moduli spaces are affine Deligne-Lusztig varieties.

The basic Newton stratum is isomorphic to the completion of an affine Deligne-Lusztig variety.

Bounds on dimension and equidimensionality are established for these varieties.

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.