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Are there complete fields of positive characteristic with non-trivial absolute value? What does calculus on them looks like? I'm aware that they have to be non-archimedean, and that the bulk of results about power series convergence will carry over, but surely there have to be some extremely weird results e.g. local expansions will be ambiguous.

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    @JyrkiLahtonen You mean $k[[X]]$ with the usual non-archimedean absolute value? Where can I read about calculus on this thing?2012-05-22

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