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Nov 24, 2010 at 22:13 comment added Kevin Buzzard You never said what the topology on $F$ was. From both the question and the answers, I gather it is the discrete topology? Indeed, if $F$ was a $p$-adic field with its usual topology then in general you can't hope for $\rho_2$ to exist in general.
Nov 24, 2010 at 0:58 comment added Henry Thank you both for your answer. Not quite sure, what I was thinking ;)
Nov 24, 2010 at 0:43 answer added Neil Strickland timeline score: 1
Nov 24, 2010 at 0:41 answer added Alex B. timeline score: 2
Nov 24, 2010 at 0:14 history asked Henry CC BY-SA 2.5