15 problems

Donovan's conjecture. Amongst all finite groups $G$ and blocks $B$ of $kG$ with defect group isomorphic to $D$, there are only finitely many Morita equivalence classes.

Bounded Morita Frobenius number conjecture. Amongst all finite groups $G$ and blocks $B$ of $kG$ with defect group isomorphic to $D$, the Morita Frobenius number…

Let $R$ be a finitely generated smooth commutative algebra over $\mathbb Z$, let $g\in\operatorname{Aut}(P_{n,R})$, and for each sufficiently large prime $p$ let $M_{g,p}$ be a bim…

Let $A_{n,\mathbb C}$ be the Weyl algebra of index $n$ over $\mathbb C$, and let $P_{n,\mathbb C}$ be the Poisson algebra of polynomial functions on the $2n$-dimensional affine sym…

Lifting conjecture. The set $X$ is a complete set of exact $H$-equivariant Morita equivalence class representatives.

Splendid Morita equivalence conjecture. The endoscopic equivalence of Theorem $$ induces a splendid Morita equivalence in the sense of Rickard.

Let $\Bbbk$ be a field, let the Morita equivalence in Theorem be the equivalence associated with the cyclotomic web construction, and let the Morita equivalence in Theorem be the e…

Let $F\colon\mathcal{S}\to\mathcal{T}$ be a morphism of limit sketches. A test Morita equivalence is a morphism of sketches that induces an equivalence … for every test sketch. Set…

Let $\mathsf{B}^{n+1}$ be a background phase and let $\mathsf{C}^{n+1}$ be an $(n+1)$D anomaly-free topological order. An MCLP lattice model over $\mathsf{B}^{n+1}$ has a local spi…

Let $F$ be an algebraically closed field of characteristic $p>0$, let $G$ be a finite group, and let $B$ be a block of $FG$ with fusion system $\mathcal{F}=\mathcal{F}_D(B)$. Write…

Let $D=(C_2)^6$ and consider purely nonprincipal blocks with defect group $D$. For each group in the following list, there is one relevant Morita equivalence class of nonprincipal…

Complementary Morita-class count conjecture.

Weight-two Morita-class count conjecture.

Let $G$ be a group, let $e$ be a block of the group algebra $\mathcal O G$, and let $(P,e_P)$ be an $e$-subpair of $G$. Let $(D,e_D)$ be a maximal $e$-subpair containing $(P,e_P)$…

Let $\mathfrak{g}$ be a restricted Lie superalgebra, let $\chi\in\mathfrak{g}_{\bar{0}}^*$ be a $p$-character with Jordan decomposition $\chi=\chi_s+\chi_n$, and let … Write…