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Jul 10, 2010 at 10:26 comment added Georges Elencwajg Yes it's true, Pedro. Since I'm responsible for some confusion, due to my original misreading of the question, allow me to sum up. a) If there are at least two primes over p, then $O_P$ is not finitely generated over $\mathbb Z_{(p)}$ : this is Keenan's answer. b) If there is only on prime over p, then $O_P$ is finitely generated over $\mathbb Z_{(p)}$. This is in the edited part of my answer (and also follows from Keith's comments, if I am not mistaken ).
Jul 9, 2010 at 12:53 vote accept Pedro Martins Rodrigues
Jul 9, 2010 at 12:46 answer added Keenan Kidwell timeline score: 6
Jul 9, 2010 at 10:43 answer added Georges Elencwajg timeline score: 2
Jul 9, 2010 at 9:31 history asked Pedro Martins Rodrigues CC BY-SA 2.5