5 problems

Let $X$ be a space, and let $d$ be the least integer such that $R_d$ is a nonconstant functor of finite degree. Assume that $d>1$. Degree-growth conjecture. At least one of the fun…

Let $X$ be a space. For each $s$, let $R_s(H^*X)$ denote the analytic functor associated with the reduced unstable module $R_s(H^*X)$. Kuhn's dichotomy conjecture. Either at least…

Let $F\colon D({\mathcal{A}})\to D({\mathcal{B}})$ be an enhanceable functor, and suppose that $(H,Q_n,\gamma)$ is a $\mathbb{P}^n$-structure on $F$. Let…

Let $F\colon D({\mathcal{A}}) \rightarrow D({\mathcal{B}})$ be a split $\mathbb{P}^n$-functor satisfying the strong monad condition. Let…

Bezrukavnikov–Etingof conjecture. The functors $\operatorname{Res}_b$ and $\operatorname{Ind}_b$ do not depend on $b$ up to non-canonical isomorphism, and similarly…