Notes on Chow rings of G/B and BG

Abstract

Let $G$ be a compact Lie group and $T$ its maximal torus. The composition of maps $H^{\ast }(BG)\to H^{\ast }(BT)\to H^{\ast }(G/T)$ is zero for positive degree, while it is far from exact. We change $H^{\ast }(G/T)$ by Chow ring $C{H}^{\ast }(X)$ for $X$ some twisted form of $G/T$, and change $H^{\ast }(BG)$ by $C{H}^{\ast }(BG)$. 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 $X$.

21 pages, 0figures

References in corpus (1)

• Mod 3 Chern classes and generators