From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2266 Path: news.gmane.org!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: Zariski spectra for rings with topology Date: Thu, 01 May 2003 11:40:28 +0100 Message-ID: <3EB0F99C.9060105@cs.bham.ac.uk> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018536 3316 80.91.229.2 (29 Apr 2009 15:22:16 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:22:16 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed May 7 14:19:43 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 May 2003 14:19:43 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19DSZK-0007R4-00 for categories-list@mta.ca; Wed, 07 May 2003 14:19:02 -0300 User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.3) Gecko/20030312 X-Accept-Language: en-us, en Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 1 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:2266 Archived-At: If R is a ring (commutative, with 1), there is a certain sense in which the structure sheaf, a local homeomorphism E -> Spec(R) (making the Zariski spectrum a local ringed space) is the free local ring over R. Can this be made to work more generally for localic rings R? (Other than in trivial ways, by taking the set of points of R.) Or for particular classes of localic rings (e.g. compact regular)? Is there a Zariski spectrum? Presumably the analogue of the structure sheaf would not be a local homeomorphism any more. Steve Vickers.