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