More Examples of Non-Rational Adjoint Groups

Abstract

We give a recursive construction to produce examples of quadratic forms q_n in the n-th power of the fundamental ideal in the Witt ring whose corresponding adjoint groups PSO(q_n) are not stably rational. Computations of the R-equivalence classes of adjoint classical groups by A.S. Merkurjev are used to show that these groups are not R-trivial. This extends earlier results of A.S. Merkurjev and P.Gille where the forms considered have non-trivial and trivial discriminants respectively.