5 problems

Martino–Priddy conjecture. The groups $G$ and $H$ have isomorphic $p$-fusion systems if and only if

Data-loss conjecture. In passing to the algebraic closure, one kills off additional data within the homotopy type, namely the data that depends on larger primes.

Let $p$ be a prime, and consider the passage from coefficients in the finite field of $p$ elements to its algebraic closure in the algebraic description of $p$-complete homotopy ty…

Let $G$ be a finite group, let $\mrm{A}(G)$ be its Burnside ring, and let $I_G\subseteq \mrm{A}(G)$ be the augmentation ideal. Write $\SS_p$ for the $p$-completed sphere and $\BG$…

Connective-cover $p$-completion conjecture. If $X$ is $p$-complete, then $\tau_{\geq 1}X$ is also $p$-complete.