The character group of k((x))

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3 total messages Started by Victor Miller Mon, 17 Aug 1992 15:47

#80

Author: Victor Miller
Date: Mon, 17 Aug 1992 15:47

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Can anyone point me to an article which discusses the group of
continuous characters of k((x)) (Laurent series in x) where k is a
finite field?  I vaguely seem to remember that using this groups
should give some sort of duality between k((x))/k[x] and k[x].
--
		Victor S. Miller
		Bitnet: VICTOR at WATSON
		Internet: victor@watson.ibm.com
		IBM, TJ Watson Research Center
		"Great artists steal; lesser artists borrow" Igor Stravinsky

Re: The character group of k((x))

#82

Author: Allan Adler
Date: Mon, 17 Aug 1992 19:44

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In article <VICTOR.92Aug17114712@terse4.watson.ibm.com> victor@watson.ibm.com (Victor Miller) writes:

   Can anyone point me to an article which discusses the group of
   continuous characters of k((x)) (Laurent series in x) where k is a
   finite field?  I vaguely seem to remember that using this groups
   should give some sort of duality between k((x))/k[x] and k[x].




See Andre Weil's book Basic Number Theory.

Allan Adler
ara@altdorf.ai.mit.edu

Re: The character group of k((x))

#83

Author: Victor Miller
Date: Mon, 17 Aug 1992 20:07

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1634 bytes

I received the following answer, which is just what I'm looking for:

Date: Mon, 17 Aug 92 21:08:24 +0200
From: Torsten Ekedahl  <teke@matematik.su.se>
Message-Id: <9208171908.AA11751@candida.matematik.su.se>
To: victor@watson.ibm.com
In-Reply-To: victor@watson.ibm.com's message of Mon, 17 Aug 1992 15:47:12 GMT
Subject: The character group of k((x))

Andre Weils Basic Number Theory (Springer Grundl d. math. Wiss. 144),
particularly II:5, discusses this. Indeed, k((x)) is self dual as
topological dual, k[[x]] is a compact subgroup with discrete quotient
and is its own annihilator for a suitable normalisation of the self
duality.

--
			Victor S. Miller
			Vnet and Bitnet:  VICTOR at WATSON
			Internet: victor@watson.ibm.com
			IBM, TJ Watson Research Center

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