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.
Calculus on complete fields of positive characteristic
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abstract-algebra
analysis
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2http://en.wikipedia.org/wiki/P-adic_analysis – 2012-05-22
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3The field of quotients of the ring of formal power series over a finite field is an example of such a field (the link given by @MarcvanLeeuwen seems to be about characteristic zero only). – 2012-05-22
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0@JyrkiLahtonen Thanks for that precision; I had been a bit too quick in posting that. I do think that the study of such fields as you mention are generally considered to be part of $p$-adic analysis. – 2012-05-22
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0@JyrkiLahtonen You mean $k[[X]]$ with the usual non-archimedean absolute value? Where can I read about calculus on this thing? – 2012-05-22