On the dimension of some union of affine Deligne-Lusztig varieties

TL;DR

This paper computes the dimension of certain unions of affine Deligne-Lusztig varieties related to moduli spaces in the context of reductive groups, expanding understanding without restrictive assumptions.

Contribution

It provides a dimension formula for unions of affine Deligne-Lusztig varieties in a broad setting, especially when $b$ is maximal neutrally acceptable.

Findings

Dimension formula for unions of affine Deligne-Lusztig varieties

Applicable to mod-$p$ reductions of Rapoport-Zink spaces

No restrictions on the reductive group beyond a mild hypothesis

Abstract

In this paper, we consider certain union $X(\mu,b)$ of affine Deligne-Lusztig varieties in the affine flag variety that arises in the study of mod-$p$ reduction of Rapoport-Zink spaces and moduli spaces of shtukas associated to a connected reductive group. Under a mild hypothesis on $\mu$, but no further restrictions on the group, we compute its dimension in the case where $b$ is the maximal neutrally acceptable element.