Smash products of E(1)-local spectra at an odd prime

Abstract

In 1996, Franke constructed a purely algebraic category that is equivalent as a triangulated category to the E(n)-local stable homotopy category for n^2+n < 2p-2. The two categories are not Quillen equivalent, and his proof uses systems of triangulated diagram categories rather than model categories. Our main result is that in the case n=1 Franke&#39;s functor maps the derived tensor product to the smash product. It can however not be an associative equivalence of monoidal categories. The first part of our paper sets up a monoidal version of Franke&#39;s systems of triangulated diagram categories and explores its properties. The second part applies these results to the specific construction of Franke&#39;s functor in order to prove the above result.