Relative discriminant norm (awaiting review)

The relative discriminant norm is $N_{K/\mathbb{Q}}(F-V)$, where $F$ is the Frobenius endomorphism, $V$ is the Verschiebung endomorphism, and $K=\mathbb{Q}[F,V]$. For this value, we have $$|N_{K/\mathbb{Q}}(F-V)|=|\Delta_R|/\Delta_{R^+}^2,$$ where $R=\mathbb{Q}[F,V]$ is the Frobenius order and $R^+=\mathbb{Z}[F+V]$ is the real order.