 Class-field unit sequence

Passing to norm limits in Artin reciprocity gives an exact sequence connecting closures of global units, local pro-$p$ units at primes over $p$, the p-ramified Iwasawa module and the unramified Iwasawa module. It explains arithmetic Iwasawa-module ranks by comparing local and global unit ranks. Roots of unity and the precise splitting conventions must be retained when seeking exact integral statements.