4 problems

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 $m=n$.

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…