6 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…

Fix a prime $p\geq 2$ and an integer $a\geq 1$ with $p\nmid a$. For integers $\rho\geq 2$ such that $m=a^2p^{2\rho}+1$ is squarefree, let … and let ${\mathcal T}_K$ be the torsion…

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 $K/\mathbb{Q}$ be a finite real Galois extension with Galois group $G$. For each sufficiently large prime $p$, let ${\mathcal T}_p$ be the $p$-ramification invariant, and let…

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-$p$…