6 problems

Let $A$ and $B$ be derived equivalent noetherian rings, and let ${\rm del}(A)$ and ${\rm del}(B)$ denote their delooping levels. The delooping-finiteness conjecture. One has … This…

Let $A$ and $B$ be Artin algebras, and suppose that they are derived equivalent. The delooping-level invariance conjecture. The finiteness of the delooping level is invariant under…

Let $A$ be the block algebra associated with the block under consideration, let $D$ be its defect group, and let $b_D$ be the corresponding block of $\mathcal{O}N_G(D)$. For a para…

Derived-equivalence classification conjecture. The blocks $\mathcal O_\xi$ and $\mathcal O_{\xi'}$ are gradably derived equivalent if and only if

Let $G$ be a finite reductive group, let $\ell$ be a prime, and suppose the assumptions (B1)–(B3) hold: $w\sigma$ is a good $d$-regular element, $\ell$ divides $|T_w|$ but not…

Deligne–Lusztig complex extension conjecture. The action of $C_G(P)\times G^{\operatorname{opp}}$ on $C$ extends, up to homotopy, to an action of