Hamacher, Paul; Viehmann, Eva

Finiteness Properties of Affine Deligne-Lusztig Varieties

Doc. Math. 25, 899-910 (2020)
DOI: 10.25537/dm.2020v25.899-910
Communicated by Otmar Venjakob


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 \(G\)-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.

Mathematics Subject Classification

14G35, 20E42, 20G25


affine Deligne-Lusztig variety, Rapoport-Zink spaces, affine flag variety


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Hamacher, Paul
Technische Universität München, Fakultät für Mathematik - M11, Boltzmannstr. 3, 85748 Garching bei München, Germany
Viehmann, Eva
Technische Universität München, Fakultät für Mathematik - M11, Boltzmannstr. 3, 85748 Garching bei München, Germany