From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5960 Path: news.gmane.org!not-for-mail From: Graham White Newsgroups: gmane.science.mathematics.categories Subject: Grothendieck's relative point of view Date: Tue, 06 Jul 2010 13:38:28 +0100 Message-ID: Reply-To: Graham White NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1278509925 29242 80.91.229.12 (7 Jul 2010 13:38:45 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 7 Jul 2010 13:38:45 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Wed Jul 07 15:38:42 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 1OWUpk-0007TH-GK for gsmc-categories@m.gmane.org; Wed, 07 Jul 2010 15:38:40 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OWUIF-0001fk-Sz for categories-list@mta.ca; Wed, 07 Jul 2010 10:04:03 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5960 Archived-At: I'm looking for some history of what seems to be called "Grothendieck's relative point of view": 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/ ]