Reduced Unitary Whitehead Groups over Function Fields of p-adic Curves

Let $F_0$ be the function field of a curve over a $p$-adic field $K,$ and let $F$ be a quadratic extension over $F_0$. Let $A$ be a central simple algebra over $F$ of period $2,$ and let $\tau$ be a $F\mathrm{/}{F}_0$-involution on $A$. We show the triviality of the reduced unitary Whitehead group $S{K}_{1}U(A,\tau )$ if $p\mathrm{\ne }2$.