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arXiv · 1902.07752

Finiteness properties of affine Deligne-Lusztig varieties

Paul Hamacher·Eva Viehmann
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Abstract

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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Paul Hamacher, Eva Viehmann. 2019-02-20. Finiteness properties of affine Deligne-Lusztig varieties. https://arxiv.org/abs/1902.07752

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