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.
Published 25 August 2015