2023/04/21 by Sanghoon Baek, Rostislav Devyatov, Baek, Sanghoon +1
Mathematics · #14C25 #16E20 #20G15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2304.10929
openalex publication_date 2023/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the canonical morphism from the Chow ring of a smooth variety X to the associated graded ring of the topological 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 generically twisted flag variety X of a semisimple group G. The conjecture was first disproved by Nobuaki Yagita for G=\mathopSpin(2n+1) with n=8, 9. Later, another counter-example to the conjecture was given by Karpenko and the first author for n=10. In this note, we provide an infinite family of counter-examples to Karpenko's conjecture for any 2-power integer n greater than 4. This generalizes Yagita's counter-example and its modification due to Karpenko for n=8.