The global structure of affine Deligne-Lusztig varieties (Q2906581)

Deligne-Lusztig varieties are certain subvarieties of the flag manifold of a reductive group, and finite coverings of these varieties can be used to study representations of reductive groups over a finite field. This article provides an overview of recent results on the global structure of affine Deligne-Lusztig varieties associated to a hyperspecial maximal compact subgroup. It contains, in particular, a discussion of a formula for the dimensions and the set of connected components of the closed affine Deligne-Lusztig varieties.NEWLINENEWLINEFor the entire collection see [Zbl 1241.00016].