4 problems

Outer-derivation conjecture. Under the hypotheses of the determinant conjecture, $D$ is outer if and only if

Let $\mathbb{K}=\mathbb{Q}(\zeta)$ be the $p^k$th cyclotomic number field, where $k\in\mathbb{N}\setminus\{1\}$ and $p$ is a rational prime, and let…

Innerness conjecture. Under the hypotheses of the determinant conjecture, if $1\le e_1\le r-1$ and $e_2\ge1$, then $D$ is inner if and only if

Let $\mathbb{K}=\mathbb{Q}(\zeta)$ be the $n$th cyclotomic number field with $n=2^r p$, where $r\in\mathbb{N}$ and $p$ is an odd rational prime, and let…