From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6575 Path: news.gmane.org!not-for-mail From: Hans Halvorson Newsgroups: gmane.science.mathematics.categories Subject: Re: Profinite groupoids Date: Mon, 7 Mar 2011 12:48:00 -0500 Message-ID: References: Reply-To: Hans Halvorson NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1299585549 28476 80.91.229.12 (8 Mar 2011 11:59:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 8 Mar 2011 11:59:09 +0000 (UTC) Cc: Categories mailing list To: "Prof. Peter Johnstone" Original-X-From: majordomo@mlist.mta.ca Tue Mar 08 12:59:05 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 1PwvZ8-00020n-3i for gsmc-categories@m.gmane.org; Tue, 08 Mar 2011 12:59:02 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:41624) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PwvYq-00076A-I7; Tue, 08 Mar 2011 07:58:44 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PwvYn-0001xb-LZ for categories-list@mlist.mta.ca; Tue, 08 Mar 2011 07:58:41 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6575 Archived-At: This question is answered in the negative in Moerdijk and Vermeulen, "Proper maps of toposes" (Remark 4.2, page 81). Hans Halvorson On Mon, Mar 7, 2011 at 5:13 AM, Prof. Peter Johnstone wrote: > 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 famil= iar > with some of your work, and since the question is one on Stone spaces, I > thought I'd ask. > > It's well known that a topological group whose underlying space is profin= ite > 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.=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)= of > finite groupoids? Is this problem open to your knowledge? > The only direct reference I could find in the literature is in the Magid'= s > paper > > Magid, Andy R. > The separable closure=A0of some commutative rings. > Trans. Amer. Math. Soc.=A0170=A0(1972), 109?124 > > where he develops the Galois theory of commutative rings. He says that it > seems to be open, but that was a long time ago. > > 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; w= hat > we do not know is whether or not the problem was previously open. > > 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. > > > Thank you, > > Alexandru [For admin and other information see: http://www.mta.ca/~cat-dist/ ]