Geodesic
Finiteness Properties of Affine Deligne-Lusztig Varieties
Documenta mathematica, Tome 25 (2020), pp. 899-910.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14G35, 20E42, 20G25
Keywords: affine Deligne-Lusztig variety, Rapoport-Zink spaces, affine flag variety 
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     author = {Hamacher, Paul and Viehmann, Eva},
     title = {Finiteness {Properties} of {Affine} {Deligne-Lusztig} {Varieties}},
     journal = {Documenta mathematica},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a41/}
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Hamacher, Paul; Viehmann, Eva. Finiteness Properties of Affine Deligne-Lusztig Varieties. Documenta mathematica, Tome 25 (2020), pp. 899-910. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a41/