Sanghoon Baek, Relationship between the Chow and Grothendieck Rings for Generic Flag Varieties

Consider the canonical morphism from the Chow ring of a smooth variety X to the associated graded ring of the coniveau filtration on the Grothendieck ring of X. In general, this morphism is not injective. However, Nikita Karpenko conjectured that these two rings are isomorphic for a generic flag variety X of a semisimple group G, where he confirmed the conjecture for a simple group G of type A or C. Recently, this conjecture was disproved by Nobuaki Yagita for some spin groups G. We will discuss further counter-examples using the K-theoretical Pieri formula for highest orthogonal grassmannians. This is joint work with Nikita Karpenko.