Inverse different
= Inverse different
{title2=$\mathfrak D_{L/K}^{-1}$}
For a finite separable extension of number fields or local fields,
$$
\mathfrak D_{L/K}^{-1}
=\{x\in L:\operatorname{Tr}_{L/K}(x\mathcal O_L)\subseteq\mathcal O_K\}.
$$
It is also called the codifferent. If $\mathcal O_L=\mathcal O_K[\alpha]$ with minimal polynomial $g$, it equals $g'(\alpha)^{-1}\mathcal O_L$.
= Codifferent
{synonym}