From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5966 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: Grothendieck's relative point of view Date: Wed, 07 Jul 2010 13:01:18 -0300 Message-ID: References: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1278553554 12920 80.91.229.12 (8 Jul 2010 01:45:54 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 8 Jul 2010 01:45:54 +0000 (UTC) Cc: categories@mta.ca To: Graham White Original-X-From: categories@mta.ca Thu Jul 08 03:45:51 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OWgBS-0007bJ-Ti for gsmc-categories@m.gmane.org; Thu, 08 Jul 2010 03:45:51 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OWfj5-0001q7-2v for categories-list@mta.ca; Wed, 07 Jul 2010 22:16:31 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5966 Archived-At: Graham White wrote: > I'm looking for some history of what seems to be called "Grothendieck's > relative point of view": What about "Grothendieck's change of base", so much used in SGA4, and extensively advocated and used by Joyal and others by considering the category of Grothendieck topoi over a given Grothendieck topos (not Sets) ?. Is not this Grothendieck's relative point of view ? I am just asking. e.d. the idea that what ostensibly seems to be an > isolated mathematical object may well be better studied by > systematically looking at families of such objects. Now Grothendieck > certainly uses it in his proof of, and generalisation of, Riemann-Roch. > And there are historical essays in various Wikis that say so. But: > i) how does he come to this idea? > ii) are there any places where he talks about it and about what it > means? What generality is it meant to apply in? > iii) does anybody before him talk about it? (In particular, there is > some explicit parametrisation involved in Weil's approach to algebraic > number theory, and the number field/function field analogy: does Weil > ever talk explicitly about this?) > > Thanks > > Graham [For admin and other information see: http://www.mta.ca/~cat-dist/ ]