Kunneth formula for graded rings associated to 𝐾-theories of Rost motives

Yagita, Nobuaki

doi:10.1090/proc/14622

Kunneth formula for graded rings associated to $K$-theories of Rost motives
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Proc. Amer. Math. Soc. 147 (2019), 4513-4526 Request permission

Abstract:

In this paper, we study the graded ring $gr^*(X)$ defined by $K$-theory of a twist flag variety $X$. In particular, the Kunneth map $gr^*(R’)\otimes gr^*(R’)\to gr^*(R)$ is studied explicitly for an original Rost motive $R’$ and a generalized Rost motive $R$. Using this, we give examples $Tor(X)^2\not =0$ for the ideal $Tor(X)$ of torsion elements in the Chow ring $CH^*(X)$.

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