Geodesic
Basic loci of Coxeter type with arbitrary parahoric level
Canadian journal of mathematics, Tome 76 (2024) no. 1, pp. 126-172

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DOI

Motivated by the desire to understand the geometry of the basic loci in the reduction of Shimura varieties, we study their “group-theoretic models”—generalized affine Deligne–Lusztig varieties—in cases where they have a particularly nice description. Continuing the work of Görtz and He (2015, Cambridge Journal of Mathematics 3, 323–353) and Görtz, He, and Nie (2019, Peking Mathematical Journal 2, 99–154), we single out the class of cases of Coxeter type, give a characterization in terms of the dimension, and obtain a complete classification. We also discuss known, new, and open cases from the point of view of Shimura varieties/Rapoport–Zink spaces.
DOI : 10.4153/S0008414X22000608
Mots-clés : Reduction of Shimura varieties, Rapoport–Zink spaces, affine Deligne–Lusztig varieties, basic loci 
Görtz, Ulrich; He, Xuhua; Nie, Sian. Basic loci of Coxeter type with arbitrary parahoric level. Canadian journal of mathematics, Tome 76 (2024) no. 1, pp. 126-172. doi: 10.4153/S0008414X22000608
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     title = {Basic loci of {Coxeter} type with arbitrary parahoric level},
     journal = {Canadian journal of mathematics},
     pages = {126--172},
     year = {2024},
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