2024/01/10 by Yong Hu, Hu, Yong, Yisheng Tian +1
Mathematics · #11E57 19B99 20G35 16K20 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2401.05017
openalex publication_date 2024/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove some triviality results for reduced Whitehead groups and reduced unitary Whitehead groups for division algebras over a henselian discrete valuation field whose residue field has virtual cohomological dimension or separable dimension ≤ 2. These results are applied to show strong approximation for isotropic absolutely almost simple simply connected groups of type A. In particular, such a group defined over the function field of a nonreal curve C/k satisfies strong approximation if the base field k is a number field, a p-adic field, ℂ( (t) ) or a two-variable function field over ℝ.