Adjoint groups over ${\mathbb{Q}}_p(X)$ and R-equivalence - revisited

Abstract

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 $p\ne 2$. We also show that for any group of type $C_n$ over $F$, the group of rational equivalence classes of $G$ over $F$ is trivial, i.e., $G(F)/R=(1)$.

11 pages