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arXiv · 1910.14541

Notes on Chow rings of G/B and BG

Nobuaki Yagita
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Abstract

Let $G$ be a compact Lie group and $T$ its maximal torus. The composition of maps $ H^*(BG)\to H^*(BT) \to H^*(G/T)$ is zero for positive degree, while it is far from exact. We change $H^*(G/T)$ by Chow ring $CH^*(X)$ for $X$ some twisted form of $G/T$, and change $H^*(BG)$ by $CH^*(BG)$. Then we see that it becomes near to exact but still not exact, in general. We also see that the difference for exactness relates to the generalized Rost motive in $X$.

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Nobuaki Yagita. 2019-10-31. Notes on Chow rings of G/B and BG. https://arxiv.org/abs/1910.14541

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