Finiteness Properties of Affine Deligne-Lusztig Varieties

  • Paul Hamacher

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

    Technische Universität München, Fakultät für Mathematik - M11, Boltzmannstr. 3, 85748 Garching bei München, Germany
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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 -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. 899–910

DOI 10.4171/DM/766