7 problems

Let $A$ be a self-injective algebra and let $\mathcal{S}$ be a weakly simple-minded system with finite cardinality in the stable module category $A$-$\mathsf{\underline{mod}}$. The…

Assume $(A,\mathfrak m)$ is a complete local complete intersection of dimension $d$ and codimension $c$, with algebraically closed residue field $k=A/\mathfrak m$. Let $X$ be an al…

Stable-category codimension conjecture. If $\operatorname{\underline{CM}}_{\leq r}(A)$ is triangle equivalent to $\operatorname{\underline{CM}}_{\leq r}(B)$, then $m=n$.

Antieau's conjecture. There is a good theory of stable $n$-categories, for $1 \leq n \leq \infty$, satisfying at least the property that stable $n$-categories, exact functors, and…

Joyal's conjecture. Every presentable stable $\infty$-category is an $\infty$-locus.

Genuine equivariant K-theory block decomposition conjecture. There is an equivalence of stable $\infty$-categories

Let $A$ be a finite-dimensional self-injective algebra, and let $\underline{\mathsf{mod}}A$ denote its stable module category. The Tachikawa conjecture. The stable category…