5 problems

Artin–Hochster conjecture. The scheme $\mathfrak C_n$ is Cohen–Macaulay.

Chevalley restriction conjecture. The homomorphism $c$ is always an isomorphism.

Let $\mathfrak{g}$ be a simple complex Lie algebra, let $G$ be the corresponding group, and let $\operatorname{Comm}(\mathfrak{g})$ be the subscheme of…

Chevalley restriction conjecture for commuting schemes. The morphism $\vartheta$ is an isomorphism. This asserts that invariant functions on commuting $n$-tuples are completely det…

Reducedness conjecture. The commuting scheme $\mathfrak{C}^d_{\mathfrak{g}}$ is reduced.