Rational equivalence on adjoint groups of type $^{1}D_n$ over field $\mathbb{Q}_P(X)$

Abstract

Let $F$ be the function field of a smooth, geometrically integral curve over a $p$-adic field with $p\neq 2.$ Let $G$ be a classical adjoint group of type $^1D_n$ defined over $F$. We show that $G(F) / R$ is trivial, where $R$ denotes {\it rational equivalence} on $G(F)$.