Local degree of a place
= Local degree of a place
For a place $v$ of a <number field> $K$, the local degree is $d_v=[K_v:\mathbb Q_v]$. Thus $d_v=1$ at a real place, $d_v=2$ at a complex place, and $d_v=e_vf_v$ at a finite place over $p$. For each rational place, the local degrees above it sum to $[K:\mathbb Q]$.