4 problems

Let $\mathcal{L}/\mathbb{Q}$ be an infinite extension. For a prime power $q$, let $\psi_q$ denote the limiting normalized number of prime ideals of norm $q$ in finite subextensions…

Let $calK/cmathbb{Q}$ be an infinite extension. For each prime power $q$, let $cpsi_q$ denote the limiting normalized number of prime ideals of norm $q$ along a tower defining…

Let $K$ be the compositum of all $\mathbb{Z}_\ell$-extensions of $\mathbb{Q}$, and let $E$ be an elliptic curve over $\mathbb{Q}$. Finite-generation conjecture. The Mordell–Weil gr…

Bottom theorem. For almost all $\boldsymbol{\sigma}\in\operatorname{Gal}(K)^e$ and every proper subfield $N\subsetneqq K_s(\boldsymbol{\sigma})$, if the extension…