On Freyd's generating hypothesis

• Autores: Mark Hovey
• Localización: Quarterly journal of mathematics, ISSN 0033-5606, Vol. 58, Nº. 1, 2007, págs. 31-45
• Idioma: inglés
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• Resumen

  • Freyd's generating hypothesis in stable homotopy theory is revisited and new consequences and equivalent forms of it are derived. A surprising such consequence is that I, the Brown¿Comenetz dual of the sphere and the source of many counterexamples in stable homotopy, is the cofibre of a self-map of a wedge of spheres. It is also shown 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 *S, is in fact true for many finite torsion spectra.