Geodesic
Finiteness Properties of Affine Deligne-Lusztig Varieties
Documenta mathematica, Tome 25 (2020), pp. 899-910
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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.
DOI : 10.4171/dm/766
Classification : 14G35, 20E42, 20G25
Mots-clés : affine Deligne-Lusztig variety, Rapoport-Zink spaces, affine flag variety 
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     author = {Paul Hamacher and Eva Viehmann},
     title = {Finiteness {Properties} of {Affine} {Deligne-Lusztig} {Varieties}},
     journal = {Documenta mathematica},
     pages = {899--910},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/766},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/766/}
}
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Paul Hamacher; Eva Viehmann. Finiteness Properties of Affine Deligne-Lusztig Varieties. Documenta mathematica, Tome 25 (2020), pp. 899-910. doi: 10.4171/dm/766

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