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How do I go about proving this? Do I have to show total boundedness (I don't know how to use the finiteness of the residue field, and this seems like something that it might pertain to).

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    I would like to look at this question, but I have no idea what notion of compactness you are working with.2012-10-18
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    Are you talking about the ring given the Krull topology or the affine scheme?2012-10-18
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    I'm only guessing but since it is complete, can you mimic the proof that the ring of p-adic integers is compact?2012-10-18

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