Cambridge Journal of Mathematics

Volume 3 (2015)

Number 3

Basic loci of Coxeter type in Shimura varieties

Pages: 323 – 353



Ulrich Görtz (Institut für Experimentelle Mathematik, Universität Duisburg-Essen, Essen, Germany)

Xuhua He (Department of Mathematics and Institute for Advanced Study, The Hong Kong University of Science and Technology, Kowloon, Hong Kong; and Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)


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 [31] and [25], 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