Finiteness Properties of Affine Deligne-Lusztig Varieties

Finiteness Properties of Affine Deligne-Lusztig Varieties

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 u...

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Veröffentlicht in:Documenta mathematica Journal der Deutschen Mathematiker-Vereinigung. 2020, Vol.25, p.899-910
Hauptverfasser: Hamacher, Paul, Viehmann, Eva
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description 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.
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title Finiteness Properties of Affine Deligne-Lusztig Varieties
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