Subject: Re: note on Generating Hypothesis From: Donald Kahn Date: Wed, 20 Jul 2005 01:44:10 -0500 thanks, this is very interesting. you do realize that if the generating hypothesis is true,then most of these injective modules will be infinitely-generated. don k. On Jul 19, 2005, at 6:59 AM, Don Davis wrote: > Subject: Another for the list > From: Mark Hovey > Date: 16 Jul 2005 07:20:36 -0400 > > I have had an insight about Freyd's generating hypothesis, to which my > last question was related. In view of the interest in the generating > hypothesis, and also to find out whether this is already known, I am > taking the unusual step of announcing this here. > > The insight is simply this: > > The p-local version of Freyd's generating hypothesis holds if and only > if the homotopy of any p-complete finite spectrum is an injective module > over the homotopy of the sphere. > An obvious corollary is that if the generating hypothesis is true, maps > from an arbitrary spectrum to a p-complete finite spectrum are > determined by their effect on homotopy. There are a couple of other > corollaries as well. > You can find a short preprint of this result at > > http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey/freyd > Mark Hovey > >