6 problems

C2-cofiniteness–rationality conjecture. If $V$ is $C_2$-cofinite, then $V$ is rational.

Let $V_L$ be a lattice vertex operator algebra, and let a parabolic-type subVOA mean a subVOA of the parabolic type considered in the paper. Cofiniteness conjecture. All parabolic-…

Let $R$ be a commutative, unital, Noetherian ring, let $I$ be an ideal of $R$, and let $N$ be a finite $R$-module. An $R$-module $H$ is $I$-cofinite if … and…

Let $\mathbb U=\mathbb V^{\otimes E}$ be the tensor product vertex operator algebra appearing above, and let $G$ be a finite group acting on $\mathbb U$ by permutations of the tens…

Let $\mathcal{W}(p)$ be the triplet vertex algebra, and let $\Gamma$ be a finite subgroup of $PSL(2,\mathbb{C})$ in the ADE classification. ADE orbifold C2-cofiniteness conjecture.…

Zhu's conjecture. Complete reducibility of $\mathbb{N}$-gradable weak modules implies $C_2$-cofiniteness.