The gamma-filtration, codimension-3 cycles, and the Rost invariant, by Skip Garibaldi and Kirill Zainoulline

Let X be the variety of Borel subgroups of a simple and strongly inner linear algebraic group G over a field k. We prove that the torsion part of the second quotient of Grothendieck's gamma-filtration on X is a cyclic group of order dividing the Dynkin index of G. As a byproduct of the proof we obtain an explicit cycle which generates this cyclic group; we provide an upper bound for the torsion of the Chow group of codimension-3 cycles on X; and we relate the generating cycle with the Rost invariant and the torsion of the respective generalized Rost motives.

Skip Garibaldi <>
Kirill Zainoulline <>