Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties

2014/08/25 by Xuhua He, He, Xuhua · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.AG #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1408.5838

19 pages

openalex publication_date 2014/08/25 · arxiv created 2015/09/24 · arxiv updated 2015/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a conjecture of Kottwitz and Rapoport on a union of (generalized) affine Deligne-Lusztig varieties X(μ, b)_J for any tamely ramified group G and its parahoric subgroup P_J. We show that X(μ, b)_J ≠ ∅ if and only if the group-theoretic version of Mazur's inequality is satisfied. In the process, we obtain a generalization of Grothendieck's conjecture on the closure relation of \s-conjugacy classes of a twisted loop group.

Citations

• A guide to the reduction modulo p of Shimura varieties
• P-alcoves and nonemptiness of affine Deligne-Lusztig varieties

Cited by

• On properness of moduli stacks of D^×-shtukas over ramified legs

Related

• On a conjecture of Kottwitz and Rapoport
• Formulas for the dimensions of some affine Deligne-Lusztig Varieties
• The dimension of some affine Deligne-Lusztig varieties
• Connectedness of affine Deligne-Lusztig varieties for unramified groups
• P-alcoves and nonemptiness of affine Deligne-Lusztig varieties