### 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 <skip@mathcs.emory.edu>

Kirill Zainoulline <kirill@uottawa.ca>