2 problems

Kochetov's conjecture. The smash product $H\#\mathbb{F}G$ is PI if and only if

Let $\mathscr{C}$ be an operad with a basepoint, let $k\geq 2$, let $l\geq 1$, and let $Y$ be a $\mathscr{C}$-space. Write $\mathcal{Z}_k[S^l,\mathscr{C}]$ for the relevant $k$-th…