On triviality of the reduced Whitehead group over Henselian fields
Archiv der Mathematik
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≤dimFq(ΓF/qΓF)≤3, the reduced Whitehead group of D is trivial.
Soman, Abhay, "On triviality of the reduced Whitehead group over Henselian fields" (2019). Journal Articles. 725.