Affine Deligne-Lusztig varieties and the action of J

TL;DR

This paper introduces a new stratification of affine Deligne-Lusztig varieties and Rapoport-Zink spaces that elucidates the connection between their geometry and automorphism group actions, unifying several known stratifications.

Contribution

It proposes a novel stratification framework that unifies various existing stratifications through a group-theoretic perspective.

Findings

New stratification of affine Deligne-Lusztig varieties and Rapoport-Zink spaces

Unified interpretation of existing stratifications

Enhanced understanding of automorphism group actions

Abstract

We propose a new stratification of the reduced subschemes of Rapoport-Zink spaces and of affine Deligne-Lusztig varieties that highlights the relation between the geometry of these spaces and the action of the associated automorphism group. We show that this provides a joint group-theoretic interpretation of well-known stratifications which only exist for special cases such as the Bruhat-Tits stratification of Vollaard and Wedhorn, the semi-module stratification of de Jong and Oort, and the locus where the a-invariant is equal to 1.