Cambridge Journal of Mathematics
Volume 3 (2015)
Basic loci of Coxeter type in Shimura varieties
Pages: 323 – 353
This paper is a contribution to the general problem of giving an explicit description of the basic locus in the reduction modulo $p$ of Shimura varieties. Motivated by  and , we classify the cases where the basic locus is (in a natural way) the union of classical Deligne–Lusztig sets associated to Coxeter elements. We show that if this is satisfied, then the Newton strata and Ekedahl–Oort strata have many nice properties.