Affine Deligne-Lusztig varieties and the action of J

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.