Subject: Two questions for the list
Date: 07 Oct 2003 07:50:02 -0400
From: Mark Hovey
Reply-To: mhovey@wesleyan.edu
To: dmd1@lehigh.edu
I have a couple of questions for the list.
1. (Asked by my colleague). Is every group the fundamental group of a
compact Hausdorff space? I know I should know the answer to this...
2. This is really an algebraic geometry question, but since I was asking
the other one...Suppose you have a map X --> Y of schemes such that the
induced map of S-valued points Sch(Spec S, X) --> Sch(Spec S, Y) is an
isomorphism for every connected ring S (in particular, every local ring
S). Must the map of schemes be an isomorphism? If every Spec A was the
coproduct of connected affine schemes Spec S this would be true, but I guess I
doubt that every Spec A is such a coproduct.
Mark Hovey