6 problems

Stable-elements conjecture. If the action of $\pi_1(|\mathcal{L}|)$ on $M$ is $p$-solvable, then the displayed isomorphism holds. This extends the established results for constrain…

Let $(S,\mathcal{F},\mathcal{L})$ be a $p$-local finite group, let $\Omega$ be an $\mathcal{F}$-characteristic $(S,S)$-biset, and let $\omega$ be an $\Omega$-endomorphism. For an a…

Sharpness for fusion systems. For all $i\geq 1$ and $j\geq 0$, the higher limits vanish:

Strong form of Oliver's conjecture.

The module-theoretic reformulation. If $V$ is an $F$-module, then there exists $1\neq g\in\Omega_1(Z(G))$ such that the minimal polynomial of the action of $g$ on $V$ divides

Miller's conjecture. Retractive transfer triples are equivalent to $p$-local finite groups, perhaps in the presence of additional structure. This proposes a purely homotopy-theoret…