Invariants of degree 3 and torsion in the Chow group of a versal flag

Abstract

We prove that the group of normalized cohomological invariants of degree 3 modulo the subgroup of semidecomposable invariants of a semisimple split linear algebraic group G is isomorphic to the torsion part of the Chow group of codimension 2 cycles of the respective versal G-flag. In particular, if G is simple, we show that this factor group is isomorphic to the group of indecomposable invariants of G. As an application, we construct nontrivial cohomological classes for indecomposable central simple algebras.

Appendix with computations for the PGO8-case is added

References in corpus (4)

• Equivariant pretheories and invariants of torsors
• Twisted gamma-filtration of a linear algebraic group
• The gamma-filtration and the Rost invariant
• Degree 3 Cohomological Invariants of Groups that are Neither Simply Connected nor Adjoint