Determinant-module formulation of the Iwasawa main conjecture

Assume the $p$-component Rubin–Stark conjecture for $L_{\chi,n}/k$ and $V_\chi$ for all $\chi\in\widehat\Delta$ and all $n$, and define $\mathcal{L}_{K_\infty/k,S,T}$ from the resulting inverse-limit Rubin–Stark elements as in the paper. Let $Q(\Lambda)$ be the total quotient ring.

Determinant-module Iwasawa main conjecture.

$$\Lambda\cdot\mathcal{L}_{K_\infty/k,S,T}=\det_\Lambda(C_{K_\infty,S,T}).$$

The paper states this as an equivalent formulation of the preceding main conjecture under the Rubin–Stark hypotheses.