4 problems

Shank–Wehlau–Broer conjecture. If $S^G$ is a direct summand of $S$ as an $S^G$-module, then $S^G$ is a polynomial ring.

Principal-plinth-ideal conjecture.

Invariant-coordinate conjecture. For every such $\phi$, there exists $\sigma\in\operatorname{T}_3(k)$ such that

Glaz's existence problem. Can one define non-Noetherian Cohen–Macaulay rings so that: (i) the definition agrees with the usual definition for Noetherian rings; (ii) coherent regula…