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 $p\ne 2.$ Let $G$ be a classical adjoint group of type ${}^1{D}_n$ defined over $F$. We show that $G(F)/R$ is trivial, where $R$ denotes {\it rational equivalence} on $G(F)$.