4 problems

The p-adic Brauer–Siegel conjecture. There exists a constant ${\mathcal C}_p({\mathcal K})$ such that

Let ${\mathcal K}_{\rm real}$ be the set of all totally real number fields, let $D_K$ be the discriminant of $K$, and fix a prime $p\geq 2$. For each $K$, let ${\mathcal T}_K$ be t…

Let $K$ be a number field satisfying the Leopoldt conjecture for every prime $p$, and let ${\mathcal T}_p$ be the torsion subgroup associated with the maximal Abelian $p$-ramified…

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-$p$…