5 problems

Let $G$ be a compact Lie group and let $BG$ be its classifying space. Kono–Yagita's even-degree conjecture. The Brown–Peterson cohomology $BP^*(BG)$ is concentrated in even degrees…

Let $G$ be a complex linear algebraic group, let $CH^i(BG)_{(p)}$ be the $p$-localized Chow group of its classifying space, and let $BP^*(BG)$ denote its Brown–Peterson cohomology.…

Totaro's conjecture. This homomorphism is an isomorphism.

Totaro's conjecture. Under these hypotheses, this map is an isomorphism. The conjecture compares the Chow ring with Brown–Peterson cohomology after localization. No resolution is s…

Let $G$ be a compact Lie group, let $BG$ be its classifying space, and let $BP^*(BG)$ denote its Brown–Peterson cohomology ring. Kono–Yagita's nilpotence conjecture. The ring…