Büyükkboduk–Lei Perrin-Riou–Stark conjecture

Let $K$ be a CM field, let $g=\tfrac12[K:\mathds{Q}]$, and fix a finite-prime-to-$p$ character $\chi:G_K\to\overline{\mathds{Q}_p}^{\times}$ satisfying the conditions in the source. Let $L$ be its field of definition, let $L_\infty$ be the composite of $L$ with the maximal $\mathds{Z}_p$-power extension of $K$, let $\Lambda=\mathds{Z}_p[\operatorname{im}\chi]\llbracket\operatorname{Gal}(L_\infty/L)\rrbracket$, and let $U_{L_\infty,\chi}=\varprojlim_F(\mathds{Z}_p\cdot\mathcal{O}_{F,S}^{\times})_\chi$. Fix a $\Lambda$-basis $b$ of $Y_K(\mathds{Z}_p{}_{L_\infty/K})_\chi$. Büyükkboduk–Lei conjecture. There exist elements $\{\mathfrak{S}_{\infty,i}^{\chi}\}_{1\leq i\leq g}$ in $U_{L_\infty,\chi}$ such that, for every finite extension $F$ of $L$ in $L_\infty$, the natural map from $\bigwedge_\Lambda^gU_{L_\infty,\chi}$ to the exterior-power bidual over $\mathds{Z}_p[\operatorname{im}\chi][\operatorname{Gal}(F/L)]$ sends

$$\bigwedge_{i=1}^{g}\mathfrak{S}_{\infty,i}^{\chi}$$

to the $\chi$-component $\eta_{F/K,S}^{b,\chi}$ of the relevant Rubin–Stark element. This conjecture predicts a universal system of units interpolating Rubin–Stark elements throughout the $p$-adic tower. Its general status is open; the source presents it as an observation concerning a conjecture of Büyükkboduk and Lei.