Basic loci in Shimura varieties of Coxeter type

2013/11/25 by Ulrich Goertz, Goertz, Ulrich, Xuhua He +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1311.6263

openalex publication_date 2013/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeVollaard-Wedhorn and \citeRapoport-Terstiege-Wilson, 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.

Citations

• A guide to the reduction modulo p of Shimura varieties

Cited by

• Fully Hodge-Newton decomposable Shimura varieties
• Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups

Related

• Basic loci of Coxeter type with arbitrary parahoric level
• Basic Loci of Positive Coxeter Type for GL_n
• Deligne-Lusztig varieties and basic EKOR strata
• The basic locus of the unitary Shimura variety with parahoric level structure, and special cycles
• Lifting Deligne-Lusztig Reduction and Geometric Coxeter Type Elements