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Andrei Lavrenov, Victor Petrov, Morava K-theory and Rost Invariant, International Mathematics Research Notices, Volume 2025, Issue 8, April 2025, rnaf101, https://doi.org/10.1093/imrn/rnaf101
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Abstract
We prove that inner forms of a variety of Borel subgroups have isomorphic motives with respect to the second Morava K-theory if and only if the corresponding Tits algebras and Rost invariants coincide. This extends Panin’s results on interrelationship of K-theory with Tits algebras to the case of cohomological invariants of degree |$3$|.
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