Re: formal power series rings and its quotient field

From: Prasanna (prasanna.sethuraman_at_gmail.com)
Date: 09/03/04 

Date: 3 Sep 2004 02:49:02 -0700

slothropuk@hotmail.com wrote in message news:<ch7c1t$ke3@odak26.prod.google.com>...
> Jyrki Lahtonen wrote:
>
> > This fits nicely into the function field picture: T^p-T=f(x)
> > is unramified at the non-poles of f(x), but is wildly
> > ramified at a pole, whenever the pole order is not divisible
> > by p (in the latter case we can reduce the pole order by a change
> > of variables, and the ramification depends on the new equation)
>
>
> There's a nice paper by Kiran Kedlaya which describes the
> whole algebraic closure - you get the wild extensions by adding in
> a bunch of generalised power series...
>
> http://www.ams.org/journal-getitem?pii=S0002993901060014
> http://front.math.ucdavis.edu/math.AG/9810142

I am wondering, why all my simple questions always have answers that
require too much of advanced, infact state of the art mathematical
results. Well... atleast the language or terms of answers are very
different from that of the question.

Thanks for the replies though. I got two things right. One, K((x)) is
not algebraically closed. Two, finding the algebraic closure is very
difficult.

Best regards,
Prasanna.

Relevant Pages

  • Re: formal power series rings and its quotient field
    ... (complex Laurent series). ... by p (in the latter case we can reduce the pole order by a change ... and the ramification depends on the new equation) ...
    (sci.math)
  • Re: formal power series rings and its quotient field
    ... > is unramified at the non-poles of f, ... > by p (in the latter case we can reduce the pole order by a change ... and the ramification depends on the new equation) ... whole algebraic closure - you get the wild extensions by adding in ...
    (sci.math)
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