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arXiv · 2602.07965

Counter-examples to a conjecture of Karpenko via truncated Brown-Peterson cohomology

Victor Petrov·Alois Wohlschlager·Egor Zolotarev
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Abstract

Let $G$ be a split semisimple linear algebraic group and let $X$ denote the generically twisted variety of Borel subgroups in $G$. Nikita Karpenko conjectured that the map from the Chow ring of $X$ to the associated graded ring of the topological filtration on the Grothendieck ring of $X$ is an isomorphism. After having been verified for many $G$, the conjecture was disproved by Nobuaki Yagita for some spinor groups. Later, other counter-examples were constructed by Baek-Karpenko and Baek-Devyatov. We present a new method for constructing counter-examples that is based on the connection of the truncated Brown-Peterson cohomology with the connective K-theory. Using this method, we disprove the conjecture for new groups, including $\mathrm{Spin}_{15}$, which is now the smallest known spinor group for which the conjecture fails.

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Victor Petrov, Alois Wohlschlager, Egor Zolotarev. 2026-02-08. Counter-examples to a conjecture of Karpenko via truncated Brown-Peterson cohomology. https://arxiv.org/abs/2602.07965

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