Adjoint groups over 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 ^2A_n and a group of type 2 D 3 ^2D_3 over the function field F F of a smooth geometrically integral curve over a p p -adic field with p ≠ 2 p \neq 2 . We also show that for any group of type C n C_n over F F , the group of rational equivalence classes of G G over F F is trivial, i.e., G ( F ) / R = ( 1 ) G(F)/R=(1) .