We obtain a class of examples of non-rational adjoint classical groups of type 2 A n and a group of type 2 D 3 over the function field F of a smooth geometrically integral curve over a p-adic field with p = 2. We also show that for any group of type C n over F , the group of rational equivalence classes of G over

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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 Fq (Γ F /qΓ F ) ≤ 3, the reduced Whitehead group of D is trivial.