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Oct 4, 2016 at 13:09 comment added S. Carnahan @DavidLoeffler Thank you. That is a very reasonable point. I will try to revise my argument.
Oct 4, 2016 at 6:56 comment added David Loeffler I don't think this answers the question, because this argument will only work if R embeds in $\mathbf{C}$. The question makes perfect sense if $R = \mathbf{F}_p$ with $p \nmid N$, for instance (and that sort of example is of fundamental importance in Mazur's work which the OP cites).
Oct 4, 2016 at 6:17 history answered S. Carnahan CC BY-SA 3.0