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).
Complete DVR with finite residue field is compact?
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commutative-algebra
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1I 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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0Are you talking about the ring given the Krull topology or the affine scheme? – 2012-10-18
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1I'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