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Oct 23, 2018 at 13:04 comment added user130124 Yes, this is Ribet's key observation which facilitated the construction of unramified extensions of cyclotomic fields to deduce the converse to Herbrand's theorem. Indeed, this is really relevant to this context.
Oct 22, 2018 at 11:24 history edited Nicolas B. CC BY-SA 4.0
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Oct 22, 2018 at 10:59 history answered Nicolas B. CC BY-SA 4.0