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3 votes

A problem in Bushnell and Henniart's book, "The local Langlands conjecture for GL(2)"

If $E/F$ is unramified and $E\neq F$ then the norm map $U_E^m/U_E^{m+1} \rightarrow U^m_F/ U^{m+1}_F$ cannot be an iso, since the groups have different order(= to the order of residue fields.)
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