= Universal norm of units in a Zp-extension
{title2=$N_\infty(E_n)=\bigcap_{m\ge n}N_{m/n}(E_m)$}
These are units that lie in every finite-layer norm image, using the p-adic closures of the unit groups. Compactness makes this intersection the image of the norm inverse limit. Local and global universal norm subgroups need not coincide. In the cyclotomic main-conjecture proof, the finite defect of global units from universal norms is related by <class field theory> to invariants of the unramified module.
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