Cambridge Journal of Mathematics

Volume 3 (2015)

Number 3

Basic loci of Coxeter type in Shimura varieties

Pages: 323 – 353

DOI: https://dx.doi.org/10.4310/CJM.2015.v3.n3.a2

Authors

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.)

Abstract

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.

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Published 25 August 2015