Counter-examples to a conjecture of Karpenko via truncated Brown-Peterson cohomology
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908820320550912 |
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| author | Petrov, Victor Wohlschlager, Alois Zolotarev, Egor |
| author_facet | Petrov, Victor Wohlschlager, Alois Zolotarev, Egor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07965 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counter-examples to a conjecture of Karpenko via truncated Brown-Peterson cohomology Petrov, Victor Wohlschlager, Alois Zolotarev, Egor Algebraic Geometry K-Theory and Homology 20G15, 14C15, 19L41 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. |
| title | Counter-examples to a conjecture of Karpenko via truncated Brown-Peterson cohomology |
| topic | Algebraic Geometry K-Theory and Homology 20G15, 14C15, 19L41 |
| url | https://arxiv.org/abs/2602.07965 |