Chow groups of products of Severi-Brauer varieties and invariants of degree 3

Abstract

We study the semi-decomposable invariants of a split semisimple group and their extension to a split reductive group by using the torsion in the codimension 2 2 Chow groups of a product of Severi-Brauer varieties. In particular, for any n ≥ 2 n\geq 2 we completely determine the degree 3 3 invariants of a split semisimple group, the quotient of ( S L 2 ) n (\mathbf {SL}_{2})^{n} by its maximal central subgroup, as well as of the corresponding split reductive group. We also provide an example illustrating that a modification of our method can be applied to find the semi-decomposable invariants of a split semisimple group of type A.