2 problems

Let $\ell$ be a rational prime, let $K$ be a number field, and let $K_\infty=K\cdot\mathbb{Q}_{\infty,\ell}$ be the cyclotomic $\mathbb{Z}_\ell$-extension of $K$. Let $A/K_\infty$…

Greenberg's conjecture. The characteristic polynomial of the $\Lambda$-module $\mathcal C^T_S(K_{\infty})$ is not divisible by $\omega$. Equivalently, its fixed submodule is finite…