Affine Deligne-Lusztig varieties are closely related to the special fibre of Newton strata in the reduction of Shimura varieties or of moduli spaces of -shtukas. In almost all cases, they are not quasi-compact. In this note we prove basic finiteness properties of affine Deligne-Lusztig varieties under minimal assumptions on the associated group. We show that affine Deligne-Lusztig varieties are locally of finite type, and prove a global finiteness result related to the natural group action. Similar results have previously been known for special situations.
Cite this article
Paul Hamacher, Eva Viehmann, Finiteness Properties of Affine Deligne-Lusztig Varieties. Doc. Math. 25 (2020), pp. 899–910DOI 10.4171/DM/766