`The stable homotopy category has a unique model at the prime 2'
Stefan Schwede
Fakultaet fuer Mathematik
Universitaet Bielefeld
33615 Bielefeld, Germany
schwede@mathematik.uni-bielefeld.de
ABSTRACT:
In a closed model category one can pass to the associated homotopy category
by formally inverting the class of weak equivalences.
But passage to the homotopy category loses information and in general
the `homotopy theory' can not be recovered from the homotopy category.
We show that in contrast to the general case, the stable homotopy category
completely determines the stable homotopy theory, at least 2-locally.
We prove a uniqueness theorem which says that there is
only one model structure (up to so called Quillen equivalence)
underlying the stable homotopy category of 2-local spectra.
This theorem is a 2-local strenghtening of a result with B. Shipley,
given in `A uniqueness theorem for stable homotopy theory', in that we use
only the triangulated structure of the stable homotopy catgory.
The earlier result with Shipley works integrally,
but needs additional structure, namely the action of the ring of
stable homotopy groups of spheres.