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Finiteness Properties of Affine Deligne-Lusztig Varieties

Authors :
Hamacher, Paul
Viehmann, Eva
Publication Year :
2020
Publisher :
Deutsche Mathematiker-Vereinigung, 2020.

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.<br />9 pages, final version to appear in Documenta Math

Details

Language :
English
Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....5ff19195dde3a121921e3b784501f05a
Full Text :
https://doi.org/10.25537/dm.2020v25.899-910