The p-component Rubin–Stark conjecture

Let $L/k$ be a finite abelian extension with Galois group $G$, let $S$ and $T$ be disjoint finite sets of places, let $V\subseteq S$ be as in the Rubin–Stark construction, and put $U_{L,S,T}=\mathbb{Z}_p\mathcal{O}_{L,S,T}^\times$. Write $\bigcap^r$ for the lattice defined using $\mathbb{Z}_p[G]$-linear alternating homomorphisms.

The p-component Rubin–Stark conjecture.

$$\epsilon_{L/k,S,T}^V\in\bigcap^r U_{L,S,T}.$$

This is the fixed-prime-$p$ version of the Rubin–Stark integrality conjecture and is used throughout the paper's Iwasawa-theoretic arguments.