The Sinnott–Kurihara integrality conjecture

Let $L/K$ be a Galois extension with Galois group $G$. Assume that $S$ contains all infinite and ramified places of $K$, that $S$ is disjoint from a finite set $T$ of places, and that $E_S^T$ is torsionfree. Let $\theta_S(0)$ denote the appropriate equivariant $L$-value and let $SKu(L/K)$ be the Sinnott–Kurihara ideal defined from these data. Sinnott–Kurihara integrality conjecture. The Sinnott–Kurihara ideal satisfies

$$SKu(L/K)\subseteq \mathcal I(G).$$

This conjecture generalizes the known abelian integrality results to non-abelian Galois extensions and is related to Fitting ideals of class groups. It is stated here without a resolution result.