More Examples of Non-Rational Adjoint Groups
Rings and Algebras
2013-07-09 v1 Group Theory
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.
Cite
@article{arxiv.1307.2143,
title = {More Examples of Non-Rational Adjoint Groups},
author = {Nivedita Bhaskhar},
journal= {arXiv preprint arXiv:1307.2143},
year = {2013}
}