4 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…

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…

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.…