4 problems

Let $p$ be a prime number and $k$ a number field. Let $\widetilde{k}$ be the maximal multiple $\mathbb{Z}_p$-extension field of $k$, let $L_{\widetilde{k}}$ be its maximal unramifi…

The probabilistic Greenberg heuristic. (i) The probability that $\delta_{\mathfrak p}(x)\geq r$ (respectively, $\delta_{\mathfrak p}(x)=0$) for every ${\mathfrak p}\mid p$ is

Let $K$ be a number field, and let $L'_{\infty}$ and $T_{\infty}$ be the fields appearing in the source's Iwasawa-theoretic construction. Generalized Greenberg conjecture. For an a…

Combined Iwasawa–Greenberg conjecture. The following groups have orders bounded independently of $n$ and $i$: (i) the $\ell$-kernels $W\!K_{4i}(F_n)$; and (ii) the imaginary compon…