On triviality of reduced Whitehead group over Henselian fields

2016/09/06 by A. Soman, Soman, A.
Mathematics · #13J15 #16K20 #19B20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1609.01403

openalex publication_date 2016/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a Henselian field of q-cohomological dimension 3, where q is a prime. Let Γ_F be the totally ordered abelian value group of F and let D be a central division algebra over F of index a power of q such that the characteristic of the residue field, F is coprime to q. We show that when 1≤dim_\mathbbF_q(Γ_F/qΓ_F)≤ 3, the reduced Whitehead group of D is trivial.

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