Abstract:

This is a recent joint work in progress with Evan Marth and Rui Xiong. We extend and generalize Chow-motivic decomposition techniques used to compute motives of hyperplane sections of twisted Milnor hypersurfaces to an arbitrary oriented cohomology in the sense of Levine-Morel. As a byproduct, we prove Rost nilpotence for all those examples of motivic decompositions.