2 problems

Let $p$ be an odd prime, let $F_\infty=\mathbb{Q}(\mu_{p^\infty},\sqrt[p^n]{m}:n\geq1)$, let $G=\operatorname{Gal}(F_\infty/\mathbb{Q})$, and let…

Let $p$ be an odd prime, let $K=\mathbb{Q}(\mu_p)$ and let $F$ be the false Tate extension layer used in the paper. Let $E/\mathbb{Q}$ be an elliptic curve with $E(K)$ finite, let…