4 problems

Let $F_{\infty}/F$ be the extension in the paper, let $G=\operatorname{Gal}(F_{\infty}/F)$, and let $H$ be the subgroup specified by the extension, with completed group ring…

Let $F_{\infty}/F$ be the $\mathbb{Z}_p^d$-extension considered in the paper, let $G=\operatorname{Gal}(F_{\infty}/F)$, and let $\Sigma_{\mathrm{ss}}$ be the set of primes where…

Let $E$ be an elliptic curve over the number field $F'$, let $F$ be a finite extension satisfying the hypotheses of the paper, and let $F^{\mathrm{cyc}}$ be the cyclotomic…

Let $\mathcal{N}(\mathcal{P})$ be the specified set of auxiliary integers, let $\mathbb{T}=T\otimes\Lambda^\iota$, and let $M_{\log}$ and $Q$ be the matrices appearing in the signe…