5 problems

Isomorphism Conjecture. For the chosen $K$- or $L$-theory, the assembly map $A_{X_G,G/H}$ should be a weak equivalence of spectra.

Piecewise-hereditary conjecture. The orbit category $\operatorname{\mathsf D^{\mathsf b}}(\operatorname{\mathsf{mod}}\Lambda)/\Sigma^n$ is triangulated if and only if $\Lambda$ is…

Piecewise-hereditary conjecture. The orbit category

Density conjecture. For each positive integer $n$, the embedding $\Delta$ is dense if and only if $\Lambda$ is piecewise hereditary.

Density conjecture. For $p\geq 7$, the above embedding is not dense. This concerns the comparison between the orbit category arising from the grading shift and the category associa…