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A counter-example by Yagita

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Karpenko,  Nikita A.
Max Planck Institute for Mathematics, Max Planck Society;

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Karpenko, N. A. (2020). A counter-example by Yagita. International Journal of Mathematics, 31(3): 2050025. doi:10.1142/S0129167X20500251.


Cite as: http://hdl.handle.net/21.11116/0000-0006-8E26-0
Abstract
According to a 2018 preprint by Nobuaki Yagita, the conjecture on a relationship between K- and Chow theories for a generically twisted flag variety of a split semisimple algebraic group G, due to the author, fails for G the spinor group Spin(17). Yagita’s tools include a Brown–Peterson version of algebraic cobordism, ordinary and connective Morava K-theories, as well as Grothendieck motives related to various cohomology theories over fields of characteristic 0. We provide a proof using only the K- and Chow theories themselves and extend the (slightly modified) example to arbitrary characteristic.