I was looking for examples for which Hasse-Norm theorem fails for abelian extensions. I found one which is given by $L=\mathbb{Q}(\sqrt{13},\sqrt{17})$ over $\mathbb{Q}$. The solution I saw shows $-1$ is a not global norm but is a local norm everywhere.
They've used in their argument that $L_{P}/\mathbb{Q}_p$ is unramified extension for all primes $p\neq 17,13$ and for all prime ideals $P$ lying over $p$. Could anyone prove this statement ? I don't really understand how to do it.