11 problems

Assume the weak exceptional zero conjecture, choose a topological generator $\gamma$ of $\Gamma$, and write $\varepsilon_\infty^\chi=(\gamma-1)^f\kappa_{\infty,\gamma}$, with botto…

Let $\varepsilon_\infty^\chi$ be the inverse-limit Rubin–Stark element, let $\mathscr{C}_{\omega_p^+}^{\mathrm{str}}$ be the explicit reciprocity operator, and let…

Let $I$ be the augmentation ideal of $\mathbb{Z}[\Gamma]$, let $epsilon$ be the element supplied by the Rubin–Stark conjecture, and let $Phi\in\iota(Lambda^n U^*)$. Let…

Let $\mathrm{Gamma}$ be the Galois group in the setup, let $U$ be the relevant group of $S$-units, and let $\mathcal{R}_{eta}$ be the regulator map associated with…

Let $k^{\mathrm{s}}$ be the maximal abelian extension of $k$ in which all places in $S_\infty(k)$ split completely, let $\Omega$ be the collection of finite ramified extensions of…

Let $k$ be the number field in the paper, let $S_infty(k)$ denote its set of infinite places, and let $\mathcal{V}$ be a subset of $S_infty(k)$. For a finite set $\mathcal{S}$ of p…

Let $\Lambda=\mathcal{O}_p[[\Gamma]]$, let $(U_\infty')^\chi$ be the $\chi$-component of the inverse limit of the $p$-unit modules, let $\varepsilon_\infty^\chi$ be the inverse-lim…

Let $\epsilon_{H,S,T,V}$ be the Rubin–Stark element and let $\epsilon_{H,S,T,V}^{\mathrm{an}}$ be the analytic Rubin–Stark element defined in the inverse-limit localized module. Le…

Assume that $(S,T,V)$ satisfies (C1), and let $\hat{\Theta}_{S,T,V}$, $p_H$, and $\hat{R}_{H/F,S,T}$ be the inverse-limit Shintani element, projection, and regulator defined in the…

Assume that $(S,T,V)$ satisfies (C1), let $\hat{\Theta}_{S,T,V,J}\in D/I_{F^{\times}}D$ be the Shintani-datum element, and let $\hat{R}_{H/F,S,T,J}$ be the corresponding regulator.…

Let $(H/F,S,T,(v_i)_i,(w_i)_i)$ be as above, let $K/F$ be a finite abelian extension unramified outside $S$ with $H\subset K$ and torsion-free $\mathcal{O}_{K,S,T}^{\times}$, and p…