I am studying Neukirch's book, Chapter II but there is an exercise in it that I feel might be incorrect. As I am new to this stuff, I hope someone can help me with this. The problem is the following:

Exercise 2. The maximal tamely ramified abelian extension V of $\mathbb{Q_p}$ is finite over the maximal unramified abelian extension T of $\mathbb{Q_p}$.

It appears to be infinite to me.


closed as off-topic by Shailesh, José Carlos Santos, A. Goodier, Brandon Carter, Matthew Leingang Apr 3 '18 at 17:17

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  • $\begingroup$ The key is that $V$ needs to be abelian as an extension of $\mathbb Q_p$, not just as an extension of $T$. $\endgroup$ – Mathmo123 Apr 3 '18 at 14:13
  • $\begingroup$ I can't answer your question, but I think the people who could help would want to know why you believe it to be infinite. $\endgroup$ – Kevin Long Apr 3 '18 at 18:18
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    $\begingroup$ I can answer your question if it is reopened. $\endgroup$ – nguyen quang do Apr 4 '18 at 9:49
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    $\begingroup$ ... As pointed out by Mathmo123, there is an interesting difference between V/T and V/Q_p $\endgroup$ – nguyen quang do Apr 4 '18 at 10:02
  • $\begingroup$ @KevinLong I think many of the people who could answer the question already understand why the OP would believe that. This question has been prematurely closed - not a great welcome for a first time poster. $\endgroup$ – Mathmo123 Apr 4 '18 at 14:41