2 problems

Splitting conjecture. There exist $R$ and $\mathbb{G}$ such that $\operatorname{Ext}(S^G;\Omega^1_{eq}(\hat{P};\hat{\mathfrak{g}}))$ is injective as an $R[\mathbb{G}]$-module, ever…

Continuity conjecture. For every such $S^G$, $\imath$, $R$, and $\mathbb{G}$, the map $\imath^*$ is continuous in the described topologies.