Tbilisi Mathematical Journal

Notes on Chow rings of flag varieties G/B and classifying spaces BG

N. Yagita

Let G be a connected compact Lie group and T its maximal torus. The composition of maps H^*(BG) → H^*(BT) → 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.


Tbilisi Mathematical Journal, Special Issue (7 - 2021), pp. 5-29