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

Abstract

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 $F/F_0$-involution on $A$. We show the triviality of the reduced unitary Whitehead group $SK_1U( A, \tau)$ if $p\neq 2$.