Non-commutative Rubin–Stark conjecture

Let $L/K$, $\Pi$, and $\Pi'$ be the fixed data, let $Sigma$ be a \subset of $Sigma(L)$ with $Sigma e Pi$, and let $p$ be a \prime such that $O^\times_{L, Pi, Pi',p}$ is torsion-free. Write $O^\times_{L, Pi, Pi',p}$ for the corresponding $p$-adic unit group and $epsilon^ Sigma_{L/K, Pi, Pi'}$ for the Rubin–Stark element. Non-commutative Rubin–Stark conjecture. For every such \prime $p$, one has

\epsilon_{L/K, Pi, Pi'}^{ \Sigma} in{\bigcap}_{ Z_p[G]}^{| \Sigma|} O_{L, Pi, Pi',p}^ ^ .

This conjecture asserts the integral, rather than merely rational, nature of the non-commutative Rubin–Stark elements. The supplied text does not state whether it is known or open.