On Freyd's generating hypothesis

Mark Hovey
mhovey@wesleyan.edu

We revisit Freyd's generating hypothesis in stable homotopy theory.  We
derive new equivalent forms of the generating hypothesis and some new
consequences of it. A surprising one is that $I$, the Brown-Comenetz
dual of the sphere and the source of many counterexamples in stable
homotopy, is the cofiber of a self map of a wedge of spheres.  We also
show that a consequence of the generating hypothesis, that the homotopy
of a finite spectrum that is not a wedge of spheres can never be
finitely generated as a module over $\pi_{*}S$, is in fact true for
finite torsion spectra.