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Dec 29, 2009 at 7:57 comment added Greg Kuperberg As you might guess, I'm not a student of local fields. As it turned out, a good summary of the basics is a good answer to the question.
Dec 27, 2009 at 18:03 comment added Kevin Buzzard This is just daft. My "answer" above is just a comment, and a review of the basics of the theory of local fields, but it has picked up votes, presumably from people who didn't understand the question but learned something from my comments! Next time someone asks a question, remind me to just list a few basic facts about one of the words in the question rather than answering it ;-)
Dec 27, 2009 at 4:43 vote accept Greg Kuperberg
Dec 26, 2009 at 9:56 comment added Kevin Buzzard Greg---perhaps a "better" moduli space would be pairs (R,pi) with R a complete DVR and pi a uniformiser. Now it seems to me that you're in much better shape. For example the mixed characteristic ones will be precisely the Eisenstein polys. Of course the stackists amongst us would tell you not to look for a moduli space at all, just to look for a stack. There is still a geometric question here---whether the functor is a stack---it's just better-hidden.
Dec 26, 2009 at 9:43 history answered Kevin Buzzard CC BY-SA 2.5