From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6573 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Profinite groupoids Date: Mon, 7 Mar 2011 10:13:53 +0000 (GMT) Message-ID: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; CHARSET=UTF-8; format=flowed Content-Transfer-Encoding: QUOTED-PRINTABLE X-Trace: dough.gmane.org 1299519571 25645 80.91.229.12 (7 Mar 2011 17:39:31 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 7 Mar 2011 17:39:31 +0000 (UTC) To: Categories mailing list Original-X-From: majordomo@mlist.mta.ca Mon Mar 07 18:39:27 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PweP0-0001pG-3X for gsmc-categories@m.gmane.org; Mon, 07 Mar 2011 18:39:26 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:34281) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PweOr-0004w8-Ta; Mon, 07 Mar 2011 13:39:17 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PweOp-00067V-FW for categories-list@mlist.mta.ca; Mon, 07 Mar 2011 13:39:15 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6573 Archived-At: I've recently received an enquiry from a graduate student (below) about whether the question "is every Stone topological groupoid a profinite groupoid?" is still open. I've never considered the question myself, and I don't recall seeing anything published on the subject. Does anyone on this list know of a reference? Peter Johnstone ---------- Forwarded message ---------- Date: Sat, 5 Mar 2011 08:46:27 +0200 From: Alexandru Chirvasitu To: P.T.Johnstone@dpmms.cam.ac.uk Subject: a technical question Dear Professor Johnstone, My name is Alexandru Chirvasitu, and I am a second year graduate student at UC Berkeley. I apologize for the imposition, but there aren't many people I know who could assist with the problem I had questions about. Being familia= r with some of your work, and since the question is one on Stone spaces, I thought I'd ask.=C2=A0 It's well known that a topological group whose underlying space is profinit= e is automatically the limit of an inverse system of finite groups. The question, briefly, is whether or not the same is true of profinite groupoids.=C2=A0By this I mean that the spaces of arrows and objects are profinite, and the source and target maps are continuous. Is it then the case that the groupoid is an inverse limit (in the category of groupoids) o= f finite groupoids? Is this problem open to your knowledge?=C2=A0 The only direct reference I could find in the literature is in the Magid's paper Magid, Andy R. The separable closure=C2=A0of some commutative rings. Trans. Amer. Math. Soc.=C2=A0170=C2=A0(1972), 109?124=C2=A0 where he develops the Galois theory of commutative rings. He says that it seems to be open, but that was a long time ago.=C2=A0 In the course of a joint project with a fellow graduate student here at Berkeley (having to do with Galois theory), we stumbled upon this problem. We think we can construct, rather naturally, plenty of counterexamples; wha= t we do not know is whether or not the problem was previously open. =C2=A0 This was pretty much it. My apologies again for taking up your time. I'm sure any input you might have will be very valuable.=C2=A0 Thank you, Alexandru=C2=A0 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]