The finiteness conjecture for the p-ramification invariants

Let $K$ be a number field, and for each prime $p$ let ${\mathcal T}_p={\rm Gal}(H^{p\rm ra}_{\!(p)}/\widehat K_{\!(p)})$, where $H^{p\rm ra}_{\!(p)}$ is the maximal Abelian pro-$p$ extension of $K$ unramified outside $p$ and $\widehat K_{\!(p)}$ is the compositum of the $\mathbb{Z}_p$-extensions of $K$. The p-ramification finiteness conjecture. The invariant $\prod_p{\mathcal T}_p$ is finite for every number field. For real fields, this is presented as a reformulation of the normalized regulator conjecture, up to a possible minus part that is trivial for sufficiently large $p$.