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Mar 28, 2016 at 21:48 comment added Will Sawin There is a little more subtlety when $p=2$, take $K=\mathbb Q$, $L= \mathbb Q(i)$, $m=1$, $n=2$, the norm map is not surjective. This can only problems for $n=2$ though as if $n=3$ or higher, $-\zeta$ has the same order as $\zeta$.
Mar 28, 2016 at 21:26 history edited John Binder CC BY-SA 3.0
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Mar 28, 2016 at 15:17 vote accept Alex
Mar 28, 2016 at 15:11 history answered John Binder CC BY-SA 3.0