Norm-compatible sequence of local units ($U_{\infty }={\underleftarrow{\lim }}_n{U}_n$)

Such a sequence $u=(u_n)$ satisfies $N_{n/n-1}{u}_n=u_{n-1}$ at every successive layer. The inverse limit uses the field norm, rather than inclusion of units from the lower field. In a p-power cyclotomic tower a Coleman power series interpolates the sequence, and its Coleman norm operator fixes the interpolating series.